{"id":3411,"date":"2023-12-01T19:35:07","date_gmt":"2023-12-01T18:35:07","guid":{"rendered":"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=3411"},"modified":"2026-04-27T12:45:06","modified_gmt":"2026-04-27T10:45:06","slug":"le-nombre-de-0-de-factorielle-n","status":"publish","type":"post","link":"https:\/\/math.univ-lyon1.fr\/dream\/?p=3411","title":{"rendered":"Le nombre de 0 de factorielle n"},"content":{"rendered":"\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/\">Accueil<\/a> \u00bb <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=3328\">Ressources p\u00e9dagogiques<\/a> \u00bb <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=77\">Des exemples de SDRP<\/a> \u00bb Le nombre de 0 de factorielle n<\/p>\r\n<h1>L&rsquo;\u00e9nonc\u00e9 de la situation<\/h1>\r\n<p>Combien y a-t-il de 0 \u00e0 la fin de n!<\/p>\r\n<p>Vid\u00e9o en construction<\/p>\r\n<h4><strong>Voici une version de l&rsquo;\u00e9nonc\u00e9 utilisable en coll\u00e8ge<\/strong><\/h4>\r\n<p>En math\u00e9matique, la factorielle d&rsquo;un nombre entier est le produit des nombres entiers (sup\u00e9rieurs \u00e0 1) qui le pr\u00e9c\u00e8dent.<\/p>\r\n<p>Par exemple :<\/p>\r\n<ul>\r\n<li>Factorielle 3 s&rsquo;\u00e9crit 1 x 2 x 3 et est \u00e9gale \u00e0 6<\/li>\r\n<li>Factorielle 4 s&rsquo;\u00e9crit 1 x 2 x 3 x 4 et est \u00e9gale \u00e0 24<\/li>\r\n<li>Factorielle 5 s&rsquo;\u00e9crit 1 x 2 x 3 x 4 x 5 et est \u00e9gale \u00e0 120<\/li>\r\n<\/ul>\r\n<p>On remarque qu&rsquo;il y a un \u00ab\u00a00\u00a0\u00bb \u00e0 la fin de Factorielle 5.<\/p>\r\n<p>Combien y aura-t-il de \u00ab\u00a00\u00a0\u00bb \u00e0 la fin de Factorielle 7 ?<br \/>Combien y aura-t-il de \u00ab\u00a00\u00a0\u00bb \u00e0 la fin de Factorielle 17 ?<br \/>Et si on se posait la question pour n&rsquo;importe quel nombre entier, comment pourrait-on faire pour trouver le nombre de \u00ab\u00a00\u00a0\u00bb \u00e0 la fin ?<\/p>\r\n<h1>Les math\u00e9matiques en jeu<\/h1>\r\n<ul>\r\n<li>\u00e9criture scientifique, \u00e9criture arrondie<\/li>\r\n<li>lien entre \u00e9criture d\u00e9cimale et d\u00e9composition en facteurs<\/li>\r\n<li>divisibilit\u00e9 par 2, par 5<\/li>\r\n<li>technique de d\u00e9nombrement<\/li>\r\n<li>r\u00e9cursivit\u00e9<\/li>\r\n<li>repr\u00e9sentation de fonctions discontinues, de suites, de courbes sur la calculatrice &#8211; \u00e9criture dans une autre base que 10, base cinq ici<\/li>\r\n<li>usage du symbole Sigma<\/li>\r\n<li>utilisation de diff\u00e9rentes calculatrices<\/li>\r\n<li>utilisation du calcul formel avec calculatrice ou logiciel<\/li>\r\n<\/ul>\r\n<h4>Analyse math\u00e9matique<\/h4>\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/04\/Nombre0Factorielle_Analyse_Maths_DREAM.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charger le document <\/a><\/p>\r\n<h4>Analyse didactique<\/h4>\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/04\/Nombre0Factorielle_Analyse_didactique_DREAM.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charger le document <\/a><\/p>\r\n<h4>Exemples de mise en \u0153uvre<\/h4>\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/04\/Nombre0Factorielle_Mise_en_oeuvre_DREAM.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charger le document <\/a><\/p>\r\n<h4>Pour aller plus loin<\/h4>\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/04\/Nombre0Factorielle_Aller_Plus_Loin_DREAM.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charger le document <\/a><\/p>\r\n<h1>Retours d&rsquo;exp\u00e9riences<\/h1>\r\n<p>Des retours d&rsquo;exp\u00e9riences partag\u00e9s par les enseignant.e.s du groupe d&rsquo;exp\u00e9rimentation qui ont mis en place ce probl\u00e8me dans le cadre d&rsquo;un enseignement fond\u00e9 sur les probl\u00e8mes<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Combien y a-t-il de 0 \u00e0 la fin de n!<\/p>\n","protected":false},"author":3,"featured_media":2506,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[106],"tags":[],"niveau":[113,114],"type_situation":[115],"theme_maths":[],"probleme_associe":[],"type-expe":[],"class_list":{"0":"post-3411","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-sdrp","8":"niveau-cycle-4","9":"niveau-lycee","10":"type_situation-sdrp","11":"czr-hentry"},"rttpg_featured_image_url":{"full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"landscape":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"portraits":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"thumbnail":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5-150x150.png",150,150,true],"medium":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5-300x171.png",300,171,true],"large":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"1536x1536":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"2048x2048":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"tc-grid-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"tc-grid":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"tc-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5-270x224.png",270,224,true],"slider-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5-393x200.png",393,200,true],"slider":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5-393x200.png",393,200,true],"tc-sq-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"tc-ws-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"tc-ws-small-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5.png",393,224,false],"tc-slider-small":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FactoNBouton2-5-393x94.png",393,94,true]},"rttpg_author":{"display_name":"St\u00e9phanie CROQUELOIS","author_link":"https:\/\/math.univ-lyon1.fr\/dream\/?author=3"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?cat=106\" rel=\"category\">SDRP<\/a>","rttpg_excerpt":"Combien y a-t-il de 0 \u00e0 la fin de 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