{"id":87,"date":"2023-07-17T12:15:31","date_gmt":"2023-07-17T12:15:31","guid":{"rendered":"https:\/\/mathority.org\/ja\/%e9%9a%8e%e4%b9%97%e8%a8%88%e7%ae%97%e6%a9%9f\/"},"modified":"2023-07-17T12:15:31","modified_gmt":"2023-07-17T12:15:31","slug":"%e9%9a%8e%e4%b9%97%e8%a8%88%e7%ae%97%e6%a9%9f","status":"publish","type":"post","link":"https:\/\/mathority.org\/ja\/%e9%9a%8e%e4%b9%97%e8%a8%88%e7%ae%97%e6%a9%9f\/","title":{"rendered":"\u96fb\u5353\u3067\u968e\u4e57\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u3067\u3059\u304b?"},"content":{"rendered":"<p>\u968e\u4e57\u306f\u3001\u611f\u5606\u7b26\u3067\u8868\u3055\u308c\u308b<strong>\u8a08\u7b97\u304c\u975e\u5e38\u306b\u7c21\u5358\u306a\u6570\u5b66\u95a2\u6570<\/strong>\u3067\u3059\u3002\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001\u3053\u306e\u6570\u5b66\u6f14\u7b97\u306e\u69cb\u6587\u306f\u3001\u6574\u6570\u306e\u5f8c\u306b\u611f\u5606\u7b26\u304c\u7d9a\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u591a\u304f\u306e\u5b66\u751f\u304c\u7591\u554f\u306b\u601d\u3046\u306e\u306f\u3001\u968e\u4e57\u306f\u4f55\u306b\u4f7f\u308f\u308c\u308b\u306e\u304b\u3001\u968e\u4e57\u3092<a href=\"https:\/\/mathority.org\/ja\" target=\"_blank\" rel=\"noreferrer noopener\">\u95a2\u6570\u96fb\u5353<\/a>\u306b\u3069\u3046\u3084\u3063\u3066\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u304b\u3001\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3053\u308c\u3089 2 \u3064\u306e\u8cea\u554f\u3092\u89e3\u6c7a\u3057\u3001\u30aa\u30f3\u30e9\u30a4\u30f3\u306e\u968e\u4e57\u6570\u8a08\u7b97\u30c4\u30fc\u30eb\u3092\u8a66\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\" id=\"calculadora-de-factoriales-online\"><span id=\"Calculadora_de_factoriales_online\">\u30aa\u30f3\u30e9\u30a4\u30f3\u4fc2\u6570\u8a08\u7b97\u6a5f<\/span><\/h2>\n<p>\u3053\u306e\u30aa\u30f3\u30e9\u30a4\u30f3\u968e\u4e57\u8a08\u7b97\u6a5f\u3092\u4f7f\u7528\u3059\u308b\u306b\u306f\u3001\u6700\u521d\u306e\u6570\u5024\u3092\u5165\u529b\u3057\u3066\u300c\u8a08\u7b97\u300d\u3092\u30af\u30ea\u30c3\u30af\u3059\u308b\u3060\u3051\u3067\u3001\u7d50\u679c\u304c\u300c\u968e\u4e57\u300d\u30dc\u30c3\u30af\u30b9\u306b\u8868\u793a\u3055\u308c\u307e\u3059\u3002<\/p>\n<p><title>\u968e\u4e57\u8a08\u7b97\u6a5f<\/title><script language=\"javascript\"><\/p>\n<p>function factorial (){\n\tvar factorial = 1;<\/p>\n<p>        for (var i=1; i <= document.getElementById ('n').value; i++){\n            factorial *= i;\n        }\n \n        document.getElementById ('resultado').value = factorial;\n}\n \n<\/script><\/p>\n<form onsubmit=\"javascript: factorial ();return (false);\">\u4eba\u6570\u3001\u500b\u6570\u3001\u7dcf\u6570\uff1a<input type=\"text\" name=\"n\" id=\"n\"><\/p>\n<p>\u968e\u4e57: <input type=\"text\" name=\"resultado\" id=\"resultado\" readonly=\"readonly\"><\/p>\n<p><input type=\"submit\" value=\"\u8a08\u7b97\u3059\u308b\"><\/p>\n<\/form>\n<h2 class=\"wp-block-heading\" id=\"que-es-un-factorial\"><span id=\"Que_es_un_factorial\">\u968e\u4e57\u3068\u306f\u4f55\u3067\u3059\u304b?<\/span><\/h2>\n<p><strong>\u6570\u5024\u306e\u968e\u4e57\u306f\u3001<\/strong> 1 \u304b\u3089\u305d\u306e\u6570\u5024\u307e\u3067\u306e\u3059\u3079\u3066\u306e<a href=\"https:\/\/mathority.org\/ja\/\u81ea\u7136\u6570\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6b63\u306e\u6574\u6570<\/a>\u306e\u7a4d\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30014 \u306e\u968e\u4e57\u3092\u77e5\u308a\u305f\u3044\u5834\u5408\u306f\u3001\u6b21\u306e\u8a08\u7b97\u3092\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u30024 <strong>! = 1 x 2 x 3 x 4 = 24<\/strong> \u3002\u5b9f\u969b\u3001\u3053\u308c\u306f\u7406\u89e3\u3059\u308b\u306e\u304c\u975e\u5e38\u306b\u7c21\u5358\u306a\u6982\u5ff5\u3067\u3059\u304c\u3001\u552f\u4e00\u8907\u96d1\u306a\u306e\u306f\u3001\u305d\u308c\u3092\u78ba\u7387\u306e\u4e16\u754c\u3067\u3069\u306e\u3088\u3046\u306b\u9069\u7528\u3059\u308b\u304b\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u6570\u5b66\u306e\u8a08\u7b97\u306b\u95a2\u3057\u3066\u306f\u3001\u639b\u3051\u7b97\u3092\u9593\u9055\u3048\u306a\u3044\u3088\u3046\u306b\u6ce8\u610f\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002<\/p>\n<p>\u968e\u4e57\u6570\u306e\u91cd\u8981\u6027\u306f<strong>\u3001\u7d44\u307f\u5408\u308f\u305b\u8ad6\u3068\u78ba\u7387<\/strong>\u306e\u6570\u5b66\u5206\u91ce\u306b\u3042\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u30ab\u30fc\u30c9\u3084\u30b5\u30a4\u30b3\u30ed\u3092\u4f7f\u3063\u3066\u3001\u8003\u3048\u3089\u308c\u308b\u3055\u307e\u3056\u307e\u306a\u9806\u5e8f\u3092\u4e26\u3079\u66ff\u3048\u305f\u308a\u6570\u3048\u305f\u308a\u3059\u308b\u5178\u578b\u7684\u306a\u6570\u5b66\u306e\u6f14\u7fd2\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u6982\u5ff5\u306f<strong>\u9806\u5217<\/strong>\u3068\u547c\u3070\u308c\u3001\u968e\u4e57\u306e\u4f7f\u7528\u3068\u5bc6\u63a5\u306b\u95a2\u9023\u3057\u3066\u3044\u307e\u3059\u3002\u5f8c\u307b\u3069\u3001\u968e\u4e57\u6570\u306e\u5fdc\u7528\u306b\u3064\u3044\u3066\u5f15\u304d\u7d9a\u304d\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"propiedades-de-los-factoriales\">\u968e\u4e57\u306e\u6027\u8cea<\/h3>\n<p>\u6b21\u306e\u30ea\u30b9\u30c8\u306b\u306f\u3001\u968e\u4e57\u6570\u306e 3 \u3064\u306e\u4e3b\u8981\u306a\u30d7\u30ed\u30d1\u30c6\u30a3\u304c\u3042\u308a\u3001\u3059\u3079\u3066\u975e\u5e38\u306b\u76f4\u611f\u7684\u3067\u3059\u3002<\/p>\n<ul>\n<li> n &gt; m \u306e\u5834\u5408\u306f\u3001n! &gt;\u79c1\uff01 \u2192 4 &gt; 3\u3001\u3057\u305f\u304c\u3063\u3066 4! &gt; 3!<\/li>\n<li> n &gt; m \u306e\u5834\u5408\u306f\u3001n! = nx (n - 1) ... (m + 1) xm! \u21925\uff01 = 3! 4x5<\/li>\n<li> n=!\u306e\u5834\u54081\u3001\u305d\u308c\u306a\u3089\u3044\u3044\u3048\uff01 &lt; ((n+1)\/2)\u00b2 \u2192 2! &lt; ((2+1)\/2)\u00b2<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\" id=\"ejemplos-de-calculo-de-un-factorial\">\u968e\u4e57\u306e\u8a08\u7b97\u4f8b<\/h3>\n<p>\u4ee5\u4e0b\u306b\u3001\u8a08\u7b97\u306e\u4ed5\u7d44\u307f\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u30011 \u304b\u3089 10 \u307e\u3067\u306e\u968e\u4e57\u306e\u8868\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<figure class=\"wp-block-table\">\n<table class=\"has-fixed-layout\">\n<tbody>\n<tr>\n<td>\u4fa1\u5024<\/td>\n<td>\u5bfe\u5fdc\u3059\u308b\u968e\u4e57<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td> 1<\/td>\n<\/tr>\n<tr>\n<td> 2<\/td>\n<td> 1\u00d72\uff1d2<\/td>\n<\/tr>\n<tr>\n<td> 3<\/td>\n<td> 1\u00d72\u00d73\uff1d6<\/td>\n<\/tr>\n<tr>\n<td> 4<\/td>\n<td> 1 \u00d7 2 \u00d7 3 \u00d7 4 = 24<\/td>\n<\/tr>\n<tr>\n<td> 5<\/td>\n<td> 1\u00d72\u00d73\u00d74\u00d75\uff1d120<\/td>\n<\/tr>\n<tr>\n<td> 6<\/td>\n<td> 1 \u00d7 2 \u00d7 3 \u00d7 4 \u00d7 5 \u00d7 6 = 720<\/td>\n<\/tr>\n<tr>\n<td> 7<\/td>\n<td> 1\u00d72\u00d73\u00d74\u00d75\u00d76\u00d77\uff1d5040<\/td>\n<\/tr>\n<tr>\n<td> 8<\/td>\n<td> 1\u00d72\u00d73\u00d74\u00d75\u00d76\u00d77\u00d78 = 40320<\/td>\n<\/tr>\n<tr>\n<td> 9<\/td>\n<td> 1 \u00d7 2 \u00d7 3 \u00d7 4 \u00d7 5 \u00d7 6 \u00d7 7 \u00d7 8 \u00d7 9 = 362880<\/td>\n<\/tr>\n<tr>\n<td>\u5341<\/td>\n<td>1 \u00d7 2 \u00d7 3 \u00d7 4 \u00d7 5 \u00d7 6 \u00d7 7 \u00d7 8 \u00d7 9 \u00d7 10 = 3628800<\/td>\n<\/tr>\n<\/tbody>\n<\/table><figcaption> 1 \u304b\u3089 10 \u307e\u3067\u306e\u968e\u4e57\u306e\u8868<\/figcaption><\/figure>\n<h3 class=\"wp-block-heading\" id=\"factorial-de-un-numero-negativo\">\u8ca0\u306e\u6570\u306e\u968e\u4e57<\/h3>\n<p>\u8ca0\u306e\u6570\u3092\u56e0\u6570\u5206\u89e3\u3059\u308b\u3053\u3068\u306f\u6570\u5b66\u7684\u306b\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u305f\u3081\u3001\u8ca0\u306e\u6570\u306e\u968e\u4e57\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3068\u8a00\u308f\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u901a\u5e38\u3001\u6df7\u4e71\u3092\u907f\u3051\u308b\u305f\u3081\u306b\u5b66\u5e74\u30ec\u30d9\u30eb\u3067\u6559\u3048\u3089\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u4e00\u5b9a\u306e\u6570\u5b66\u30ec\u30d9\u30eb\u306b\u9054\u3057\u3001<strong>\u30aa\u30a4\u30e9\u30fc\u306e\u300c\u30ac\u30f3\u30de\u95a2\u6570\u300d<\/strong>\u3092\u5b66\u3076\u3068\u3001\u3042\u3089\u3086\u308b\u8ca0\u306e\u6570\u3001\u5c0f\u6570\u3001\u5206\u6570\u306e\u968e\u4e57\u3092\u8a08\u7b97\u3067\u304d\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306f\u6b21\u306e\u7a4d\u5206\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"370\" height=\"194\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/fonction-gamma-deuler.webp\" data-src=\"\" alt=\"\u30aa\u30a4\u30e9\u30fc\u30ac\u30f3\u30de\u95a2\u6570\" class=\"wp-image-4665 lazyload\" srcset=\"\" sizes=\"auto, \"><figcaption>\u30aa\u30a4\u30e9\u30fc\u30ac\u30f3\u30de\u95a2\u6570<\/figcaption><\/figure>\n<\/div>\n<p>\u305d\u3057\u3066\u3044\u3064\u3082\u306e\u3088\u3046\u306b\u65b9\u7a0b\u5f0f<strong>n! = \u0393(n+1)<\/strong>\u306e\u5834\u5408\u3001\u30ac\u30f3\u30de\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u3042\u3089\u3086\u308b\u30bf\u30a4\u30d7\u306e\u968e\u4e57\u3092\u5e38\u306b\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 0.25 \u306e\u968e\u4e57\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u5b9f\u969b\u306b\u306f \u0393(1.25) \u306e\u5024\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u305d\u308c\u4ee5\u6765\u30010.25\uff01 = \u0393(0.25 + 1) = \u0393(1.25)\u3002<\/p>\n<h3 class=\"wp-block-heading\" id=\"factorial-de-0\"> 0\u306e\u968e\u4e57<\/h3>\n<p>\u30bc\u30ed\u306e\u968e\u4e57\u306f<strong>0 \u306a\u306e\u3067\u5c11\u3057\u7570\u306a\u308a\u307e\u3059\u3002 = 1<\/strong> \u3002\u3053\u308c\u306b\u306f\u5c11\u3057\u9a5a\u304b\u308c\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u305d\u306e\u7406\u7531\u3092\u8aac\u660e\u3059\u308b\u3068\u3059\u3050\u306b\u7406\u89e3\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u3002\u305d\u3053\u3067\u3001\u5148\u307b\u3069\u8aac\u660e\u3057\u305f\u968e\u4e57\u306e\u5b9a\u7fa9\u3092\u3082\u3046\u4e00\u5ea6\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u300c\u6570\u5024\u306e\u968e\u4e57\u306f\u30011 \u304b\u3089\u305d\u306e\u6570\u5024\u307e\u3067\u306e\u3059\u3079\u3066\u306e\u6b63\u306e\u6574\u6570\u306e\u7a4d\u3067\u3059\u3002\u300d\u3055\u3066\u3001\u305d\u3046\u306f\u8a00\u3063\u3066\u3082\u3001 <strong>0 \u3092\u793a\u3059\u4e00\u9023\u306e\u6570\u5f0f\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002 = 1<\/strong> :<\/p>\n<p> 2\uff01 = 3!\/3 = 6\/3 = 2<\/p>\n<p> 1! = 2!\/2 = 2\/2 = 1<\/p>\n<p> 0! = 1!\/1 = 1\/1 = 1<\/p>\n<h2 class=\"wp-block-heading\" id=\"como-calcular-un-factorial-en-la-calculadora-cientifica\"><span id=\"Como_calcular_un_factorial_en_la_calculadora_cientifica\">\u95a2\u6570\u96fb\u5353\u3067\u968e\u4e57\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u3067\u3059\u304b?<\/span><\/h2>\n<p>\u5927\u304d\u306a\u6570\u5024\u306e\u968e\u4e57\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u5834\u5408\u306f\u3001<strong>\u96fb\u5353\u306e\u968e\u4e57\u95a2\u6570<\/strong>\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u5f37\u304f\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u305d\u3046\u3057\u306a\u3044\u3068\u3001\u975e\u5e38\u306b\u591a\u304f\u306e\u4e57\u7b97\u3092\u89e3\u304f\u306e\u306b\u6c17\u304c\u72c2\u3063\u3066\u3057\u307e\u3046\u53ef\u80fd\u6027\u304c\u3042\u308b\u304b\u3089\u3067\u3059\u3002\u3053\u3046\u3059\u308b\u3053\u3068\u3067\u3001\u6642\u9593\u3092\u7bc0\u7d04\u3067\u304d\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u3053\u308c\u3089\u306e\u8a08\u7b97\u3092\u96fb\u5353\u306e\u78ba\u7387\u95a2\u6570\u3068\u7d44\u307f\u5408\u308f\u305b\u3066\u3001\u6570\u5b66\u7684\u8a08\u7b97\u3092\u3088\u308a\u9069\u5207\u306b\u30a4\u30f3\u30bf\u30fc\u30ea\u30fc\u30d6\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u30bf\u30a4\u30d7\u306e\u8a08\u7b97\u3092\u89e3\u304f\u306b\u306f\u3001\u8a08\u7b97\u6a5f\u3067\u968e\u4e57\u8a18\u53f7<strong>n!\u3001x!<\/strong>\u3092\u898b\u3064\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<strong>\u3069\u3061\u3089\u304b\uff01<\/strong> \u3002\u3082\u3061\u308d\u3093\u3001\u6570\u5024 + 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href=\"https:\/\/mathority.org\/ja\/\u96fb\u5353\u306e\u4f7f\u3044\u65b9\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u95a2\u6570\u96fb\u5353\u306e\u4f7f\u7528<\/a>\u306b\u95a2\u3059\u308b\u8a18\u4e8b\u3082\u53c2\u7167\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\" id=\"factorial-en-la-calculadora-casio-fx-991\"> <span id=\"Factorial_en_la_calculadora_Casio_FX-991\">Casio FX-991 \u96fb\u5353\u306e\u968e\u4e57<\/span><\/h2>\n<p>\u8a18\u4e8b\u306e\u6700\u5f8c\u306b\u3001 <a href=\"https:\/\/mathority.org\/ja\" target=\"_blank\" rel=\"noreferrer noopener\">Casio FX-911SPX 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&hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ja\/%e9%9a%8e%e4%b9%97%e8%a8%88%e7%ae%97%e6%a9%9f\/\"> <span class=\"screen-reader-text\">\u96fb\u5353\u3067\u968e\u4e57\u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u3067\u3059\u304b?<\/span> \u3082\u3063\u3068\u8aad\u3080 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