{"id":1337,"date":"2026-03-06T12:15:05","date_gmt":"2026-03-06T10:15:05","guid":{"rendered":"https:\/\/blog.edu.turku.fi\/allu\/?page_id=1337"},"modified":"2026-03-30T14:04:48","modified_gmt":"2026-03-30T11:04:48","slug":"alkuluvut","status":"publish","type":"page","link":"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/lukuteoria\/alkuluvut\/","title":{"rendered":"Alkuluvut"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" href=\"https:\/\/blog.edu.turku.fi\/allu\/sivu-1\/lukuteoria\/\" style=\"background-color:#d6d6ff\">Palaa takaisin<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Alkuluvut<\/h2>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p class=\"has-text-align-left\">Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoihin, perus ja vaikeisiin teht\u00e4viin.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#e6f3b7\">Helppo<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color has-text-align-center wp-element-button\" style=\"background-color:#d6d6ff\">Perus<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-black-color has-text-color has-background has-link-color wp-element-button\" style=\"background-color:#fcd8c8\">Vaikea<\/a><\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 1.<\/strong> Todista, onko luku alkuluku vai yhdistetty luku.<\/h3>\n\n\n\n<p><strong>a) <\/strong>17<br><strong>b)<\/strong> 27<br><strong>c) <\/strong>71<br><strong>d) <\/strong>221<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-1&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-1-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-1\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-1\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-1-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a) <\/strong><math data-latex=\"\\sqrt{17}\\approx4,123\"><semantics><mrow><msqrt><mn>17<\/mn><\/msqrt><mo>\u2248<\/mo><mn>4,123<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{17}\\approx4,123<\/annotation><\/semantics><\/math> , todistamiseen riitt\u00e4\u00e4 saatua lukua pienemm\u00e4t alkuluvut eli 2 ja 3.<br><math data-latex=\"\\frac{17}{2}=8,5\"><semantics><mrow><mfrac><mn>17<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>8,5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{17}{2}=8,5<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{17}{3}\\approx5,667\"><semantics><mrow><mfrac><mn>17<\/mn><mn>3<\/mn><\/mfrac><mo>\u2248<\/mo><mn>5,667<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{17}{3}\\approx5,667<\/annotation><\/semantics><\/math><br>vastaus: Luku 17 on alkuluku, koska kokeilluista jakolaskuista mik\u00e4\u00e4n ei mene tasan.<\/p>\n\n\n\n<p><strong>b)<\/strong> <math data-latex=\"\\sqrt{27}\\approx5,196\"><semantics><mrow><msqrt><mn>27<\/mn><\/msqrt><mo>\u2248<\/mo><mn>5,196<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{27}\\approx5,196<\/annotation><\/semantics><\/math> , todistamiseen riitt\u00e4\u00e4 saatua lukua pienemm\u00e4t alkuluvut eli 2, 3 ja 5.<br><math data-latex=\"\\frac{27}{2}=13,5\"><semantics><mrow><mfrac><mn>27<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>13,5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{27}{2}=13,5<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{27}{3}=9\"><semantics><mrow><mfrac><mn>27<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{27}{3}=9<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{27}{5}=5,4\"><semantics><mrow><mfrac><mn>27<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>5,4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{27}{5}=5,4<\/annotation><\/semantics><\/math><br>vastaus: Luku 27 ei ole alkuluku, koska se on jaollinen luvulla 3.<\/p>\n\n\n\n<p><strong>c)<\/strong> <math data-latex=\"\\sqrt{71}\\approx8,426\"><semantics><mrow><msqrt><mn>71<\/mn><\/msqrt><mo>\u2248<\/mo><mn>8,426<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{71}\\approx8,426<\/annotation><\/semantics><\/math> , todistamiseen riitt\u00e4\u00e4 saatua lukua pienemm\u00e4t alkuluvut eli 2, 3, 5 ja 7.<br><math data-latex=\"\\frac{71}{2}=35{,}5\"><semantics><mrow><mfrac><mn>71<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>35,5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{71}{2}=35{,}5<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{71}{3}\\approx23,667\"><semantics><mrow><mfrac><mn>71<\/mn><mn>3<\/mn><\/mfrac><mo>\u2248<\/mo><mn>23,667<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{71}{3}\\approx23,667<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{71}{5}=14,2\"><semantics><mrow><mfrac><mn>71<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>14,2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{71}{5}=14,2<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{71}{7}\\approx10,143\"><semantics><mrow><mfrac><mn>71<\/mn><mn>7<\/mn><\/mfrac><mo>\u2248<\/mo><mn>10,143<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{71}{7}\\approx10,143<\/annotation><\/semantics><\/math><br>vastaus: Luku 71 on alkuluku, koska kokeilluista jakolaskuista yksik\u00e4\u00e4n ei mene tasan.<\/p>\n\n\n\n<p><strong>d)<\/strong> <math data-latex=\"\\sqrt{221}\\approx14,866\"><semantics><mrow><msqrt><mn>221<\/mn><\/msqrt><mo>\u2248<\/mo><mn>14,866<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt{221}\\approx14,866<\/annotation><\/semantics><\/math>, todistamiseen riitt\u00e4\u00e4 lukua 14 pienemm\u00e4t alkuluvut eli 2, 3, 5, 7, 11 ja 13.<br><math data-latex=\"\\frac{221}{2}=110,5\"><semantics><mrow><mfrac><mn>221<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>110,5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{221}{2}=110,5<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{221}{3}\\approx73,667\"><semantics><mrow><mfrac><mn>221<\/mn><mn>3<\/mn><\/mfrac><mo>\u2248<\/mo><mn>73,667<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{221}{3}\\approx73,667<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{221}{5}=44,2\"><semantics><mrow><mfrac><mn>221<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>44,2<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{221}{5}=44,2<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{221}{7}\\approx31,571\"><semantics><mrow><mfrac><mn>221<\/mn><mn>7<\/mn><\/mfrac><mo>\u2248<\/mo><mn>31,571<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{221}{7}\\approx31,571<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{221}{11}\\approx20,09\"><semantics><mrow><mfrac><mn>221<\/mn><mn>11<\/mn><\/mfrac><mo>\u2248<\/mo><mn>20,09<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{221}{11}\\approx20,09<\/annotation><\/semantics><\/math><br><br><math data-latex=\"\\frac{221}{13}=17\"><semantics><mrow><mfrac><mn>221<\/mn><mn>13<\/mn><\/mfrac><mo>=<\/mo><mn>17<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{221}{13}=17<\/annotation><\/semantics><\/math><br>vastaus: Luku 221 ei ole alkuluku, koska se on jaollinen luvulla 13.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 2.1.<\/strong> Jaa annetut luvut alkutekij\u00f6ihin.<\/h3>\n\n\n\n<p><strong>a)<\/strong> 66<br><strong>b)<\/strong> 90<br><strong>c) <\/strong>24<br><strong>d)<\/strong> 20<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-2&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-2-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-2\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-2\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-2-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a) <\/strong><math data-latex=\"2\\cdot3\\cdot11\"><semantics><mrow><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>11<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2\\cdot3\\cdot11<\/annotation><\/semantics><\/math><br><strong>b) <\/strong><math data-latex=\"2\\cdot3\\cdot3\\cdot5\"><semantics><mrow><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2\\cdot3\\cdot3\\cdot5<\/annotation><\/semantics><\/math><br><strong>c) <\/strong><math data-latex=\"2\\cdot2\\cdot2\\cdot3\"><semantics><mrow><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2\\cdot2\\cdot2\\cdot3<\/annotation><\/semantics><\/math><br><strong>d) <\/strong><math data-latex=\"3\\cdot5\\cdot5\"><semantics><mrow><mn>3<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">3\\cdot5\\cdot5<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 2.2. <\/strong>Tutki, onko <strong>teht\u00e4v\u00e4n 1.1.<\/strong> kohdat jaollisia seuraavilla luvuilla<\/h3>\n\n\n\n<p><strong>a) <\/strong>6<br><strong>b)<\/strong> 9<br><strong>c) <\/strong>15<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-3&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-3-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-3\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-3\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-3-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a)<\/strong> Luvulla 6 jaollisia ovat a, b ja c.<br><strong>b)<\/strong> Luvulla 9 jaollinen on b.<br><strong>c) <\/strong>Luvulla 15 jaollisia ovat b ja d.<\/p>\n\n\n\n<ol style=\"list-style-type:lower-alpha\" class=\"wp-block-list\">\n<li><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 3.<\/strong> Toteuta Eratostheneen seula ja selvit\u00e4 sen avulla kaikki alkuluvut v\u00e4lilt\u00e4 2-20.<\/h3>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-4&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#e6f3b7\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-4-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-4\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-4\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-4-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"927\" height=\"130\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-27.png\" alt=\"Eratostheneen seulaa varten luotu taulukko. Luvut 2-20 jokainen omassa solussa.\" class=\"wp-image-2513\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-27.png 927w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-27-300x42.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-27-768x108.png 768w\" sizes=\"auto, (max-width: 927px) 100vw, 927px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"915\" height=\"423\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-26.png\" alt=\"\" class=\"wp-image-2512\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-26.png 915w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-26-300x139.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-26-768x355.png 768w\" sizes=\"auto, (max-width: 915px) 100vw, 915px\" \/><\/figure>\n\n\n\n<p>Vastaus: Alkulukuja ovat 2, 3, 5, 7, 11, 13, 17 ja 19.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 4.<\/strong> Selvit\u00e4 annettujen lukujen suurin yhteinen tekij\u00e4 eli syt alkulukuhajotelman avulla.<\/h3>\n\n\n\n<p><strong>a)<\/strong> 9, 36<br><strong>b)<\/strong> 35, 55<br><strong>c)<\/strong> 156, 221, 1170<br><strong>d)<\/strong> 105, 252, 343<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-5&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-5-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-5\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-5\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-5-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a) <\/strong>vastaus: 9<br><math data-latex=\"9=3\\cdot3=3^2\"><semantics><mrow><mn>9<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">9=3\\cdot3=3^2<\/annotation><\/semantics><\/math><br><math data-latex=\"36=2\\cdot18=2\\cdot2\\cdot9=2\\cdot2\\cdot3\\cdot3=2^2\\cdot3^2\"><semantics><mrow><mn>36<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>18<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">36=2\\cdot18=2\\cdot2\\cdot9=2\\cdot2\\cdot3\\cdot3=2^2\\cdot3^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>b) <\/strong>vastaus: 5<br><math data-latex=\"35=5\\cdot6=5\\cdot3\\cdot2=2\\cdot3\\cdot5\"><semantics><mrow><mn>35<\/mn><mo>=<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>6<\/mn><mo>=<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">35=5\\cdot6=5\\cdot3\\cdot2=2\\cdot3\\cdot5<\/annotation><\/semantics><\/math><br><math data-latex=\"55=5\\cdot11\"><semantics><mrow><mn>55<\/mn><mo>=<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>11<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">55=5\\cdot11<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>c)<\/strong> vastaus: 13<br><math data-latex=\"156=2\\cdot78=2\\cdot2\\cdot39=2\\cdot2\\cdot3\\cdot13=2^2\\cdot3\\cdot13\"><semantics><mrow><mn>156<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>78<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>39<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>13<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>13<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">156=2\\cdot78=2\\cdot2\\cdot39=2\\cdot2\\cdot3\\cdot13=2^2\\cdot3\\cdot13<\/annotation><\/semantics><\/math><br><math data-latex=\"221=13\\cdot17\"><semantics><mrow><mn>221<\/mn><mo>=<\/mo><mn>13<\/mn><mo>\u22c5<\/mo><mn>17<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">221=13\\cdot17<\/annotation><\/semantics><\/math><br><math data-latex=\"1170=2\\cdot585=2\\cdot5\\cdot117=2\\cdot5\\cdot13\\cdot9=2\\cdot5\\cdot13\\cdot3\\cdot3=2\\cdot3^2\\cdot5\\cdot13\"><semantics><mrow><mn>1170<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>585<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>117<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>13<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>13<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>13<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">1170=2\\cdot585=2\\cdot5\\cdot117=2\\cdot5\\cdot13\\cdot9=2\\cdot5\\cdot13\\cdot3\\cdot3=2\\cdot3^2\\cdot5\\cdot13<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>d)<\/strong> vastaus: 7<br><math data-latex=\"105=5\\cdot21=5\\cdot7\\cdot3=3\\cdot5\\cdot7\"><semantics><mrow><mn>105<\/mn><mo>=<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>21<\/mn><mo>=<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">105=5\\cdot21=5\\cdot7\\cdot3=3\\cdot5\\cdot7<\/annotation><\/semantics><\/math><br><math data-latex=\"252=2\\cdot126=2\\cdot2\\cdot63=2\\cdot2\\cdot7\\cdot9=2\\cdot2\\cdot7\\cdot3\\cdot3=2^2\\cdot3^2\\cdot7\"><semantics><mrow><mn>252<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>126<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>63<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">252=2\\cdot126=2\\cdot2\\cdot63=2\\cdot2\\cdot7\\cdot9=2\\cdot2\\cdot7\\cdot3\\cdot3=2^2\\cdot3^2\\cdot7<\/annotation><\/semantics><\/math><br><math data-latex=\"343=7\\cdot49=7\\cdot7\\cdot7=7^3\"><semantics><mrow><mn>343<\/mn><mo>=<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>49<\/mn><mo>=<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>=<\/mo><msup><mn>7<\/mn><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">343=7\\cdot49=7\\cdot7\\cdot7=7^3<\/annotation><\/semantics><\/math><br><br><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 5.<\/strong> Selvit\u00e4 annettujen lukujen pienin yhteinen monikerta eli pym alkulukuhajotelman avulla.<\/h3>\n\n\n\n<p><strong>a) <\/strong>9, 36<br><strong>b) <\/strong>28, 98<br><strong>c) <\/strong>24, 120, 189<br><strong>d)<\/strong> 12, 18, 27 <\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-6&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-6-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-6\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-6\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-6-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a) <\/strong>vastaus: 36<br><math data-latex=\"9=3\\cdot3=3^2\"><semantics><mrow><mn>9<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">9=3\\cdot3=3^2<\/annotation><\/semantics><\/math><br><math data-latex=\"36=2\\cdot18=2\\cdot2\\cdot9=2\\cdot2\\cdot3\\cdot3=2^2\\cdot3^2\"><semantics><mrow><mn>36<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>18<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">36=2\\cdot18=2\\cdot2\\cdot9=2\\cdot2\\cdot3\\cdot3=2^2\\cdot3^2<\/annotation><\/semantics><\/math><br><math data-latex=\"pym(9,36)=2^2\\cdot3^2=4\\cdot9=36\"><semantics><mrow><mi>p<\/mi><mi>y<\/mi><mi>m<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>9,36<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>4<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">pym(9,36)=2^2\\cdot3^2=4\\cdot9=36<\/annotation><\/semantics><\/math> tai <math data-latex=\"pym(9,36)=\\frac{9\\cdot36}{syt(9,36)}=\\frac{324}{9}=36\"><semantics><mrow><mi>p<\/mi><mi>y<\/mi><mi>m<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>9,36<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mn>9<\/mn><mo>\u22c5<\/mo><mn>36<\/mn><\/mrow><mrow><mi>s<\/mi><mi>y<\/mi><mi>t<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>9,36<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>324<\/mn><mn>9<\/mn><\/mfrac><mo>=<\/mo><mn>36<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">pym(9,36)=\\frac{9\\cdot36}{syt(9,36)}=\\frac{324}{9}=36<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>b) <\/strong>vastaus: 196<br><math data-latex=\"28=2\\cdot14=2\\cdot2\\cdot7=2^2\\cdot7\"><semantics><mrow><mn>28<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>14<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">28=2\\cdot14=2\\cdot2\\cdot7=2^2\\cdot7<\/annotation><\/semantics><\/math><br><math data-latex=\"98=2\\cdot49=2\\cdot7\\cdot7=2\\cdot7^2\"><semantics><mrow><mn>98<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>49<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><msup><mn>7<\/mn><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">98=2\\cdot49=2\\cdot7\\cdot7=2\\cdot7^2<\/annotation><\/semantics><\/math><br><math data-latex=\"pym(28,98)=2^2\\cdot7^2=4\\cdot49=196\"><semantics><mrow><mi>p<\/mi><mi>y<\/mi><mi>m<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>28,98<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><msup><mn>7<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>4<\/mn><mo>\u22c5<\/mo><mn>49<\/mn><mo>=<\/mo><mn>196<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">pym(28,98)=2^2\\cdot7^2=4\\cdot49=196<\/annotation><\/semantics><\/math> tai <math data-latex=\"pym(28,98)=\\frac{28\\cdot98}{syt(28,98)}=\\frac{2&nbsp;744}{14}=196\"><semantics><mrow><mi>p<\/mi><mi>y<\/mi><mi>m<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>28,98<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mrow><mn>28<\/mn><mo>\u22c5<\/mo><mn>98<\/mn><\/mrow><mrow><mi>s<\/mi><mi>y<\/mi><mi>t<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>28,98<\/mn><mo form=\"postfix\" stretchy=\"false\" lspace=\"0em\" rspace=\"0em\">)<\/mo><\/mrow><\/mfrac><mo>=<\/mo><mfrac><mn>2744<\/mn><mn>14<\/mn><\/mfrac><mo>=<\/mo><mn>196<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">pym(28,98)=\\frac{28\\cdot98}{syt(28,98)}=\\frac{2&nbsp;744}{14}=196<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>c)<\/strong> vastaus: 216<br><math data-latex=\"24=2\\cdot12=2\\cdot2\\cdot6=2\\cdot2\\cdot2\\cdot3=2^3\\cdot3\"><semantics><mrow><mn>24<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>12<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>6<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>\u22c5<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">24=2\\cdot12=2\\cdot2\\cdot6=2\\cdot2\\cdot2\\cdot3=2^3\\cdot3<\/annotation><\/semantics><\/math><br><math data-latex=\"120=2\\cdot60=2\\cdot2\\cdot30=2\\cdot2\\cdot2\\cdot15=2\\cdot2\\cdot2\\cdot3\\cdot5=2^3\\cdot3\\cdot5\"><semantics><mrow><mn>120<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>60<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>30<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>15<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">120=2\\cdot60=2\\cdot2\\cdot30=2\\cdot2\\cdot2\\cdot15=2\\cdot2\\cdot2\\cdot3\\cdot5=2^3\\cdot3\\cdot5<\/annotation><\/semantics><\/math><br><math data-latex=\"189=3\\cdot63=3\\cdot3\\cdot21=3\\cdot3\\cdot3\\cdot7=3^3\\cdot7\"><semantics><mrow><mn>189<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>63<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>21<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>7<\/mn><mo>=<\/mo><msup><mn>3<\/mn><mn>3<\/mn><\/msup><mo>\u22c5<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">189=3\\cdot63=3\\cdot3\\cdot21=3\\cdot3\\cdot3\\cdot7=3^3\\cdot7<\/annotation><\/semantics><\/math><br><math data-latex=\"pym(24,120,189)=2^3\\cdot3^3=8\\cdot27=216\"><semantics><mrow><mi>p<\/mi><mi>y<\/mi><mi>m<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>24,120,189<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>3<\/mn><\/msup><mo>=<\/mo><mn>8<\/mn><mo>\u22c5<\/mo><mn>27<\/mn><mo>=<\/mo><mn>216<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">pym(24,120,189)=2^3\\cdot3^3=8\\cdot27=216<\/annotation><\/semantics><\/math> <\/p>\n\n\n\n<p><strong>d) <\/strong>vastaus: 108<br><math data-latex=\"12=2\\cdot6=2\\cdot2\\cdot3=2^2\\cdot3\"><semantics><mrow><mn>12<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>6<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">12=2\\cdot6=2\\cdot2\\cdot3=2^2\\cdot3<\/annotation><\/semantics><\/math><br><math data-latex=\"18=2\\cdot9=2\\cdot3\\cdot3=2\\cdot3^2\"><semantics><mrow><mn>18<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><mn>2<\/mn><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">18=2\\cdot9=2\\cdot3\\cdot3=2\\cdot3^2<\/annotation><\/semantics><\/math><br><math data-latex=\"27=3\\cdot9=3\\cdot3\\cdot3=3^3\"><semantics><mrow><mn>27<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>9<\/mn><mo>=<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>\u22c5<\/mo><mn>3<\/mn><mo>=<\/mo><msup><mn>3<\/mn><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">27=3\\cdot9=3\\cdot3\\cdot3=3^3<\/annotation><\/semantics><\/math><br><math data-latex=\"pym(12,18,27)=2^2\\cdot3^3=4\\cdot27=108\"><semantics><mrow><mi>p<\/mi><mi>y<\/mi><mi>m<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mn>12,18,27<\/mn><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>\u22c5<\/mo><msup><mn>3<\/mn><mn>3<\/mn><\/msup><mo>=<\/mo><mn>4<\/mn><mo>\u22c5<\/mo><mn>27<\/mn><mo>=<\/mo><mn>108<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">pym(12,18,27)=2^2\\cdot3^3=4\\cdot27=108<\/annotation><\/semantics><\/math><\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 6. <\/strong>Toteuta Eratostheneen seula ja selvit\u00e4 sen avulla kaikki alkuluvut v\u00e4lilt\u00e4 2000-2026.<\/h3>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-7&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#d6d6ff\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-7-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-7\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-7\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-7-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Malli ratkaisu:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"563\" height=\"479\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-21.png\" alt=\"Kuvassa esitell\u00e4\u00e4n vaihe vaiheelta Eratostheneen seula, kun koitetaan l\u00f6yt\u00e4\u00e4 alkuluvut v\u00e4lilt\u00e4 2000-2026.\" class=\"wp-image-2488\" style=\"width:759px;height:auto\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-21.png 563w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-21-300x255.png 300w\" sizes=\"auto, (max-width: 563px) 100vw, 563px\" \/><\/figure>\n\n\n\n<p>vastaus: 2003, 2011 ja 2017<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4  7.<\/strong> Mersennen alkuluvut.<\/h3>\n\n\n\n<p>Tutki seuraavilla eksponentteja:<br>p=2,&nbsp;3,&nbsp;4,&nbsp;5,&nbsp;7,&nbsp;11<br><br>a) Laske vastaavat Mersennen luvut <math data-latex=\"M_p=2^p-1\"><semantics><mrow><msub><mi>M<\/mi><mi>p<\/mi><\/msub><mo>=<\/mo><msup><mn>2<\/mn><mi>p<\/mi><\/msup><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_p=2^p-1<\/annotation><\/semantics><\/math><br>b) Todista, mitk\u00e4 a-kohdan luvuista ovat alkulukuja.<br>c) Mik\u00e4 ehto eksponentille <math><semantics><mrow><mi>p<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math> t\u00e4ytyy toteutua, jotta <math><semantics><mrow><msub><mi>M<\/mi><mi>p<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">M_p<\/annotation><\/semantics><\/math>\u200b voi olla alkuluku? Selit\u00e4 omin sanoin.<\/p>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-8&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-8-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-8\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-8\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-8-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p><strong>a)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>p<\/td><td><math data-latex=\"2^p\"><semantics><msup><mn>2<\/mn><mi>p<\/mi><\/msup><annotation encoding=\"application\/x-tex\">2^p<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"M_p=2^p-1\"><semantics><mrow><msub><mi>M<\/mi><mi>p<\/mi><\/msub><mo>=<\/mo><msup><mn>2<\/mn><mi>p<\/mi><\/msup><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_p=2^p-1<\/annotation><\/semantics><\/math><\/td><\/tr><tr><td>2<\/td><td><math data-latex=\"2^2=4\"><semantics><mrow><msup><mn>2<\/mn><mn>2<\/mn><\/msup><mo>=<\/mo><mn>4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2^2=4<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"M_2=4-1=3\"><semantics><mrow><msub><mi>M<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mn>4<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_2=4-1=3<\/annotation><\/semantics><\/math><\/td><\/tr><tr><td>3<\/td><td><math data-latex=\"2^3=8\"><semantics><mrow><msup><mn>2<\/mn><mn>3<\/mn><\/msup><mo>=<\/mo><mn>8<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2^3=8<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"M_3=8-1=7\"><semantics><mrow><msub><mi>M<\/mi><mn>3<\/mn><\/msub><mo>=<\/mo><mn>8<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_3=8-1=7<\/annotation><\/semantics><\/math><\/td><\/tr><tr><td>4<\/td><td><math data-latex=\"2^4=16\"><semantics><mrow><msup><mn>2<\/mn><mn>4<\/mn><\/msup><mo>=<\/mo><mn>16<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2^4=16<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"M_4=16-1=15\"><semantics><mrow><msub><mi>M<\/mi><mn>4<\/mn><\/msub><mo>=<\/mo><mn>16<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_4=16-1=15<\/annotation><\/semantics><\/math><\/td><\/tr><tr><td>5<\/td><td><math data-latex=\"2^5=32\"><semantics><mrow><msup><mn>2<\/mn><mn>5<\/mn><\/msup><mo>=<\/mo><mn>32<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2^5=32<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"M_5=32-1=31\"><semantics><mrow><msub><mi>M<\/mi><mn>5<\/mn><\/msub><mo>=<\/mo><mn>32<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>31<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_5=32-1=31<\/annotation><\/semantics><\/math><\/td><\/tr><tr><td>7<\/td><td><math data-latex=\"2^7=128\"><semantics><mrow><msup><mn>2<\/mn><mn>7<\/mn><\/msup><mo>=<\/mo><mn>128<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2^7=128<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"M_7=128-1=127\"><semantics><mrow><msub><mi>M<\/mi><mn>7<\/mn><\/msub><mo>=<\/mo><mn>128<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>127<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_7=128-1=127<\/annotation><\/semantics><\/math><\/td><\/tr><tr><td>11<\/td><td><math data-latex=\"2^{11}=2048\"><semantics><mrow><msup><mn>2<\/mn><mn>11<\/mn><\/msup><mo>=<\/mo><mn>2048<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2^{11}=2048<\/annotation><\/semantics><\/math><\/td><td><math data-latex=\"M_{11}=2048-1=2047\"><semantics><mrow><msub><mi>M<\/mi><mn>11<\/mn><\/msub><mo>=<\/mo><mn>2048<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>2047<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_{11}=2048-1=2047<\/annotation><\/semantics><\/math><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div style=\"height:19px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><strong>b)<\/strong><br><math data-latex=\"M_2=3\"><semantics><mrow><msub><mi>M<\/mi><mn>2<\/mn><\/msub><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_2=3<\/annotation><\/semantics><\/math> on alkuluku<br><math data-latex=\"M_3=7\"><semantics><mrow><msub><mi>M<\/mi><mn>3<\/mn><\/msub><mo>=<\/mo><mn>7<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_3=7<\/annotation><\/semantics><\/math> on alkuluku<br><math data-latex=\"M_4=15\"><semantics><mrow><msub><mi>M<\/mi><mn>4<\/mn><\/msub><mo>=<\/mo><mn>15<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_4=15<\/annotation><\/semantics><\/math> ei ole alkuluku, koska <math data-latex=\"\\frac{15}{3}=5\"><semantics><mrow><mfrac><mn>15<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{15}{3}=5<\/annotation><\/semantics><\/math><br><math data-latex=\"M_5=31\"><semantics><mrow><msub><mi>M<\/mi><mn>5<\/mn><\/msub><mo>=<\/mo><mn>31<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_5=31<\/annotation><\/semantics><\/math> on alkuluku<br><math data-latex=\"M_7=127\"><semantics><mrow><msub><mi>M<\/mi><mn>7<\/mn><\/msub><mo>=<\/mo><mn>127<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_7=127<\/annotation><\/semantics><\/math> on alkuluku<br><math data-latex=\"M_{11}=2047\"><semantics><mrow><msub><mi>M<\/mi><mn>11<\/mn><\/msub><mo>=<\/mo><mn>2047<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">M_{11}=2047<\/annotation><\/semantics><\/math> ei ole alkuluku, koska <math data-latex=\"\\frac{2047}{23}=89\"><semantics><mrow><mfrac><mn>2047<\/mn><mn>23<\/mn><\/mfrac><mo>=<\/mo><mn>89<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2047}{23}=89<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p><strong>c) <\/strong> Jotta <math data-latex=\"M_p\"><semantics><msub><mi>M<\/mi><mi>p<\/mi><\/msub><annotation encoding=\"application\/x-tex\">M_p<\/annotation><\/semantics><\/math> voi olla alkuluku tulee my\u00f6s <math data-latex=\"p\"><semantics><mi>p<\/mi><annotation encoding=\"application\/x-tex\">p<\/annotation><\/semantics><\/math>:n olla alkuluku. <em>(HUOM! Kaikki alkuluvut eiv\u00e4t kuitenkaan tuota Mersennen alkulukua.)<\/em><br><br><\/p>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:43px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading\" style=\"font-size:18px\"><strong>Teht\u00e4v\u00e4 8.<\/strong> Selvit\u00e4 suurin nelinumeroinen alkuluku.<\/h3>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-9&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-9-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-9\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">VINKKI!<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-9\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-9-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Voit k\u00e4ytt\u00e4\u00e4 apuna esimerkiksi Eratostheneen seulaa ja rajata tutkittavan alueen 9900-9999 tai seuloa luvut suurimmasta nelinumeroisesta luvusta alasp\u00e4in.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-12&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-12-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-12\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Vastaus<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-12\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-12-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p>Esimerkki ratkaisuja:<\/p>\n\n\n\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group is-layout-constrained wp-block-group-is-layout-constrained\">\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-10&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-10-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-10\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Erathostheneen seula<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-10\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-10-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"955\" height=\"443\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-24.png\" alt=\"\" class=\"wp-image-2491\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-24.png 955w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-24-300x139.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/image-24-768x356.png 768w\" sizes=\"auto, (max-width: 955px) 100vw, 955px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"955\" height=\"445\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135242.png\" alt=\"\" class=\"wp-image-2492\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135242.png 955w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135242-300x140.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135242-768x358.png 768w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135242-750x350.png 750w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135242-642x300.png 642w\" sizes=\"auto, (max-width: 955px) 100vw, 955px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"957\" height=\"448\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135420.png\" alt=\"\" class=\"wp-image-2493\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135420.png 957w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135420-300x140.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135420-768x360.png 768w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135420-750x350.png 750w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135420-642x300.png 642w\" sizes=\"auto, (max-width: 957px) 100vw, 957px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"964\" height=\"447\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135612.png\" alt=\"\" class=\"wp-image-2494\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135612.png 964w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135612-300x139.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135612-768x356.png 768w\" sizes=\"auto, (max-width: 964px) 100vw, 964px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"966\" height=\"445\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135917.png\" alt=\"\" class=\"wp-image-2495\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135917.png 966w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135917-300x138.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-135917-768x354.png 768w\" sizes=\"auto, (max-width: 966px) 100vw, 966px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"968\" height=\"446\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-140403.png\" alt=\"\" class=\"wp-image-2496\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-140403.png 968w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-140403-300x138.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-140403-768x354.png 768w\" sizes=\"auto, (max-width: 968px) 100vw, 968px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"989\" height=\"446\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-145024.png\" alt=\"\" class=\"wp-image-2502\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-145024.png 989w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-145024-300x135.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-145024-768x346.png 768w\" sizes=\"auto, (max-width: 989px) 100vw, 989px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"928\" height=\"450\" src=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-144138.png\" alt=\"\" class=\"wp-image-2498\" srcset=\"https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-144138.png 928w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-144138-300x145.png 300w, https:\/\/blog.edu.turku.fi\/allu\/files\/2026\/03\/Nayttokuva-2026-03-25-144138-768x372.png 768w\" sizes=\"auto, (max-width: 928px) 100vw, 928px\" \/><\/figure>\n\n\n\n<p>Vastaus: Suurin nelinumeroinen alkuluku on <strong>9973<\/strong>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div data-wp-context=\"{ &quot;autoclose&quot;: false, &quot;accordionItems&quot;: [] }\" data-wp-interactive=\"core\/accordion\" role=\"group\" class=\"wp-block-accordion is-layout-flow wp-block-accordion-is-layout-flow\">\n<div data-wp-class--is-open=\"state.isOpen\" data-wp-context=\"{ &quot;id&quot;: &quot;accordion-item-11&quot;, &quot;openByDefault&quot;: false }\" data-wp-init=\"callbacks.initAccordionItems\" data-wp-on-window--hashchange=\"callbacks.hashChange\" class=\"wp-block-accordion-item is-layout-flow wp-block-accordion-item-is-layout-flow\">\n<h3 class=\"wp-block-accordion-heading has-background has-medium-font-size\" style=\"background-color:#fcd8c8\"><button aria-expanded=\"false\" aria-controls=\"accordion-item-11-panel\" data-wp-bind--aria-expanded=\"state.isOpen\" data-wp-on--click=\"actions.toggle\" data-wp-on--keydown=\"actions.handleKeyDown\" id=\"accordion-item-11\" type=\"button\" class=\"wp-block-accordion-heading__toggle\"><span class=\"wp-block-accordion-heading__toggle-title\">Seulonta suurimmasta luvusta pienemp\u00e4\u00e4n, kunnes l\u00f6ytyy alkuluku<\/span><span class=\"wp-block-accordion-heading__toggle-icon\" aria-hidden=\"true\">+<\/span><\/button><\/h3>\n\n\n\n<div inert aria-labelledby=\"accordion-item-11\" data-wp-bind--inert=\"!state.isOpen\" id=\"accordion-item-11-panel\" role=\"region\" class=\"wp-block-accordion-panel is-layout-flow wp-block-accordion-panel-is-layout-flow\">\n<p> <math data-latex=\"\\frac{9999}{3}=3333\"><semantics><mrow><mfrac><mn>9999<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3333<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9999}{3}=3333<\/annotation><\/semantics><\/math>,  <math data-latex=\"\\frac{9998}{2}=4999\"><semantics><mrow><mfrac><mn>9998<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4999<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9998}{2}=4999<\/annotation><\/semantics><\/math>,  <math data-latex=\"\\frac{9997}{13}=769\"><semantics><mrow><mfrac><mn>9997<\/mn><mn>13<\/mn><\/mfrac><mo>=<\/mo><mn>769<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9997}{13}=769<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9996}{2}=4998\"><semantics><mrow><mfrac><mn>9996<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4998<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9996}{2}=4998<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9995}{5}=1999\"><semantics><mrow><mfrac><mn>9995<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>1999<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9995}{5}=1999<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9994}{2}=4997\"><semantics><mrow><mfrac><mn>9994<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4997<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9994}{2}=4997<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9993}{3}=3331\"><semantics><mrow><mfrac><mn>9993<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3331<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9993}{3}=3331<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9992}{2}=4996\"><semantics><mrow><mfrac><mn>9992<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4996<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9992}{2}=4996<\/annotation><\/semantics><\/math>, <br><br><math data-latex=\"\\frac{9991}{97}=103\"><semantics><mrow><mfrac><mn>9991<\/mn><mn>97<\/mn><\/mfrac><mo>=<\/mo><mn>103<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9991}{97}=103<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9990}{2}=4995\"><semantics><mrow><mfrac><mn>9990<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4995<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9990}{2}=4995<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9989}{7}=1427\"><semantics><mrow><mfrac><mn>9989<\/mn><mn>7<\/mn><\/mfrac><mo>=<\/mo><mn>1427<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9989}{7}=1427<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9988}{2}=4994\"><semantics><mrow><mfrac><mn>9988<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4994<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9988}{2}=4994<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9987}{3}=3329\"><semantics><mrow><mfrac><mn>9987<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3329<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9987}{3}=3329<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9986}{2}=4993\"><semantics><mrow><mfrac><mn>9986<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4993<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9986}{2}=4993<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9985}{5}=1997\"><semantics><mrow><mfrac><mn>9985<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>1997<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9985}{5}=1997<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9984}{2}=4992\"><semantics><mrow><mfrac><mn>9984<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4992<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9984}{2}=4992<\/annotation><\/semantics><\/math>,<br><br><math data-latex=\"\\frac{9983}{67}=149\"><semantics><mrow><mfrac><mn>9983<\/mn><mn>67<\/mn><\/mfrac><mo>=<\/mo><mn>149<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9983}{67}=149<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9982}{2}=4991\"><semantics><mrow><mfrac><mn>9982<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4991<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9982}{2}=4991<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9981}{3}=3327\"><semantics><mrow><mfrac><mn>9981<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3327<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9981}{3}=3327<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9980}{2}=4990\"><semantics><mrow><mfrac><mn>9980<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4990<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9980}{2}=4990<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9979}{17}=587\"><semantics><mrow><mfrac><mn>9979<\/mn><mn>17<\/mn><\/mfrac><mo>=<\/mo><mn>587<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9979}{17}=587<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9978}{2}=4989\"><semantics><mrow><mfrac><mn>9978<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4989<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9978}{2}=4989<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9977}{11}=907\"><semantics><mrow><mfrac><mn>9977<\/mn><mn>11<\/mn><\/mfrac><mo>=<\/mo><mn>907<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9977}{11}=907<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9976}{2}=4988\"><semantics><mrow><mfrac><mn>9976<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4988<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9976}{2}=4988<\/annotation><\/semantics><\/math>,<br><br><math data-latex=\"\\frac{9975}{5}=1995\"><semantics><mrow><mfrac><mn>9975<\/mn><mn>5<\/mn><\/mfrac><mo>=<\/mo><mn>1995<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9975}{5}=1995<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9974}{2}=4987\"><semantics><mrow><mfrac><mn>9974<\/mn><mn>2<\/mn><\/mfrac><mo>=<\/mo><mn>4987<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9974}{2}=4987<\/annotation><\/semantics><\/math>, <strong>9973<\/strong> ei ole jaollinen kuin itsell\u00e4\u00e4n ja 1.<\/p>\n\n\n\n<p>Vastaus: <strong>9973<\/strong><\/p>\n\n\n\n<div style=\"height:19px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>T\u00e4ll\u00e4 tekniikalla voidaan my\u00f6s sulkea pois suoraan 2 ja 5 jaolliset luvut, koska ne havaitaan helposti:<\/p>\n\n\n\n<p> <math data-latex=\"\\frac{9999}{3}=3333\"><semantics><mrow><mfrac><mn>9999<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3333<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9999}{3}=3333<\/annotation><\/semantics><\/math>,  <math data-latex=\"\\frac{9997}{13}=769\"><semantics><mrow><mfrac><mn>9997<\/mn><mn>13<\/mn><\/mfrac><mo>=<\/mo><mn>769<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9997}{13}=769<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9993}{3}=3331\"><semantics><mrow><mfrac><mn>9993<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3331<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9993}{3}=3331<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9991}{97}=103\"><semantics><mrow><mfrac><mn>9991<\/mn><mn>97<\/mn><\/mfrac><mo>=<\/mo><mn>103<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9991}{97}=103<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9989}{7}=1427\"><semantics><mrow><mfrac><mn>9989<\/mn><mn>7<\/mn><\/mfrac><mo>=<\/mo><mn>1427<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9989}{7}=1427<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9987}{3}=3329\"><semantics><mrow><mfrac><mn>9987<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3329<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9987}{3}=3329<\/annotation><\/semantics><\/math>,<br><br><math data-latex=\"\\frac{9983}{67}=149\"><semantics><mrow><mfrac><mn>9983<\/mn><mn>67<\/mn><\/mfrac><mo>=<\/mo><mn>149<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9983}{67}=149<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9981}{3}=3327\"><semantics><mrow><mfrac><mn>9981<\/mn><mn>3<\/mn><\/mfrac><mo>=<\/mo><mn>3327<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9981}{3}=3327<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9979}{17}=587\"><semantics><mrow><mfrac><mn>9979<\/mn><mn>17<\/mn><\/mfrac><mo>=<\/mo><mn>587<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9979}{17}=587<\/annotation><\/semantics><\/math>, <math data-latex=\"\\frac{9977}{11}=907\"><semantics><mrow><mfrac><mn>9977<\/mn><mn>11<\/mn><\/mfrac><mo>=<\/mo><mn>907<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{9977}{11}=907<\/annotation><\/semantics><\/math>, <strong>9973<\/strong> ei ole jaollinen kuin itsell\u00e4\u00e4n ja 1.<\/p>\n\n\n\n<p>Vastaus: <strong>9973<\/strong><\/p>\n\n\n\n<p><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Alkuluvut Teht\u00e4v\u00e4t on jaoteltu v\u00e4rin mukaan helppoihin, perus ja vaikeisiin teht\u00e4viin. Teht\u00e4v\u00e4 1. Todista, onko luku alkuluku vai yhdistetty luku. a) 17b) 27c) 71d) 221 Teht\u00e4v\u00e4 2.1. Jaa annetut luvut alkutekij\u00f6ihin. a) 66b) 90c) 24d) 20 Teht\u00e4v\u00e4 2.2. Tutki, onko<\/p>\n","protected":false},"author":3745,"featured_media":0,"parent":95,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1337","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1337","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/users\/3745"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/comments?post=1337"}],"version-history":[{"count":28,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1337\/revisions"}],"predecessor-version":[{"id":2669,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/1337\/revisions\/2669"}],"up":[{"embeddable":true,"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/pages\/95"}],"wp:attachment":[{"href":"https:\/\/blog.edu.turku.fi\/allu\/wp-json\/wp\/v2\/media?parent=1337"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}