{"id":62,"date":"2023-09-17T07:21:09","date_gmt":"2023-09-17T07:21:09","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%95%b0%e5%ad%97%e7%9a%84%e9%98%b6%e4%b9%98%e5%87%bd%e6%95%b0\/"},"modified":"2023-09-17T07:21:09","modified_gmt":"2023-09-17T07:21:09","slug":"%e6%95%b0%e5%ad%97%e7%9a%84%e9%98%b6%e4%b9%98%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%95%b0%e5%ad%97%e7%9a%84%e9%98%b6%e4%b9%98%e5%87%bd%e6%95%b0\/","title":{"rendered":"\u6570\u5b57\u7684\u9636\u4e58\u51fd\u6570"},"content":{"rendered":"<p>\u672c\u9875\u89e3\u91ca\u4ec0\u4e48\u662f\u6570\u5b57\u7684\u9636\u4e58\u53ca\u5176\u8ba1\u7b97\u65b9\u6cd5\u3002\u6b64\u5916\uff0c\u8fd8\u63d0\u4f9b\u4e86\u51e0\u4e2a\u793a\u4f8b\u548c\u4e00\u4e2a\u5305\u542b\u6700\u5e38\u7528\u9636\u4e58\u503c\u7684\u8868\u683c\u3002\u5b83\u8fd8\u6559\u6388\u5982\u4f55\u4f7f\u7528\u8ba1\u7b97\u5668\u8ba1\u7b97\u6570\u5b57\u7684\u9636\u4e58\u3002\u6700\u540e\uff0c\u8bf4\u660e\u4e86\u9636\u4e58\u7684\u5e94\u7528\u548c\u6027\u8d28\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-factorial-de-un-numero\"><\/span>\u4e00\u4e2a\u6570\u7684\u9636\u4e58\u662f\u4ec0\u4e48\uff1f <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-background\" style=\"background-color:#ffebee\">\u5728\u6570\u5b66\u4e2d\uff0c<strong>\u6570\u5b57\u7684\u9636\u4e58<\/strong>\u7b49\u4e8e\u4ece 1 \u5230\u8be5\u6570\u5b57\u7684\u6240\u6709\u6b63\u6574\u6570\u7684\u4e58\u79ef\u3002\u6b64\u5916\uff0c\u6570\u5b57\u7684\u9636\u4e58\u7531\u6570\u5b57\u540e\u9762\u7684\u611f\u53f9\u53f7 (!) \u8868\u793a\u3002 <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/factorielle-dun-nombre.jpg\" alt=\"\u4e00\u4e2a\u6570\u7684\u9636\u4e58\" class=\"wp-image-1870\" width=\"152\" height=\"152\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p>\u4f8b\u5982\uff0c\u8981\u786e\u5b9a\u6570\u5b57<em>n<\/em>\u7684\u9636\u4e58\uff08\u4e5f\u79f0\u4e3a\u9636\u4e58<em>n<\/em> \uff09\uff0c\u60a8\u5fc5\u987b\u5c06\u6570\u5b57<em>n<\/em>\u4e58\u4ee5\u5b83\u524d\u9762\u7684\u6240\u6709\u6574\u6570\uff08\u4ece 1 \u5f00\u59cb\uff09\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49a90a973e9e420c44502cd9c8a870ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n! = 1 \\cdot 2 \\cdot 3 \\cdots (n-2) \\cdot (n-1) \\cdot n\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"265\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-calcular-el-factorial-de-un-numero\"><\/span>\u5982\u4f55\u8ba1\u7b97\u6570\u5b57\u7684\u9636\u4e58<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u6570\u5b57\u9636\u4e58\u7684\u542b\u4e49\uff0c\u8ba9\u6211\u4eec\u901a\u8fc7\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u5982\u4f55\u786e\u5b9a\u4efb\u4f55\u9636\u4e58\uff1a<\/p>\n<ul>\n<li>\u8ba1\u7b97 4 \u7684\u9636\u4e58\uff1a<\/li>\n<\/ul>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u5176\u6570\u5b66\u5b9a\u4e49\u4e2d\u770b\u5230\u7684\u90a3\u6837\uff0c\u6570\u5b57\u7684\u9636\u4e58\u76f8\u5f53\u4e8e\u6240\u6709\u5c0f\u4e8e\u6216\u7b49\u4e8e\u8be5\u6570\u5b57\u7684\u6b63\u6574\u6570\u7684\u4e58\u79ef\u3002\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97 4 \u7684\u9636\u4e58\uff0c\u6211\u4eec\u9700\u8981\u5c06\u6570\u5b57 1\u30012\u30013 \u548c 4 \u76f8\u4e58\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2d8186d4343b8a2ffc6567e323dab6d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4! = 1 \\cdot 2 \\cdot 3 \\cdot 4 =24\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"153\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64 4 \u7684\u9636\u4e58\u5f97\u5230 24\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-factoriales-de-numeros\"><\/span>\u6570\u5b57\u7684\u9636\u4e58\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u5b8c\u6210\u5bf9\u6570\u5b57\u9636\u4e58\u6982\u5ff5\u7684\u7406\u89e3\uff0c\u6211\u4eec\u7ed9\u60a8\u63d0\u4f9b\u4e00\u4e2a\u8ba1\u7b97\u4e0d\u540c\u6570\u5b57\u7684\u9636\u4e58\u7684\u793a\u4f8b\uff1a<\/p>\n<ul>\n<li> 3 \u7684\u9636\u4e58\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-325e737422d7201e476c4a60bfe966f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3! = 1 \\cdot 2 \\cdot 3 =6\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"122\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> 5 \u7684\u9636\u4e58\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3b9936934f623ae1f84b1d8d33b5a6a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5! = 1 \\cdot 2 \\cdot 3 \\cdot 4 \\cdot 5=120\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"184\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> 6 \u7684\u9636\u4e58\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bb40997fdc483ae843ffed87eb17a70c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6! = 1 \\cdot 2 \\cdot 3 \\cdot 4 \\cdot 5 \\cdot 6=720\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"205\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> 1 \u7684\u9636\u4e58\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78b2257245ff53ae4369f3b71629ae83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1! = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"44\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u6570\u5b57 1 \u7684\u9636\u4e58\u7b49\u4e8e 1\uff0c\u56e0\u4e3a\u4e58\u4ee5 1 \u5c31\u8db3\u591f\u4e86\u3002<\/p>\n<ul>\n<li> 0 \u7684\u9636\u4e58\uff1a<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-255b29d39824041f4d334887daa9d55d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0! = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"45\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u662f\u7684\uff0c\u597d\u5427\uff0c\u4ee4\u4eba\u60ca\u8bb6\u7684\u662f\uff0c0 \u7684\u9636\u4e58\u4e0d\u7b49\u4e8e 0\uff0c\u800c\u662f\u7b49\u4e8e 1\u3002\u8fd9\u5bf9\u4f60\u6765\u8bf4\u53ef\u80fd\u6709\u70b9\u5947\u602a\uff0c\u56e0\u4e3a\u7406\u8bba\u4e0a\u4f60\u5fc5\u987b\u5c06 0 \u4e58\u4ee5 1\u3002\u4f46\u662f\uff0c\u6309\u7167\u60ef\u4f8b\uff0c0\uff01 =1\uff0c\u56e0\u4e3a<a href=\"https:\/\/es.wikipedia.org\/wiki\/Producto_vac%C3%ADo\" target=\"_blank\" rel=\"noreferrer noopener\">\u4ea7\u54c1\u5c5e\u6027\u4e3a\u7a7a<\/a>\u3002\u6211\u4eec\u7ed9\u60a8\u7559\u4e0b\u8fd9\u4e2a\u94fe\u63a5\uff0c\u4ee5\u9632\u60a8\u60f3\u4e86\u89e3\u66f4\u591a\u4fe1\u606f\uff0c\u5c3d\u7ba1\u60a8\u77e5\u9053\u539f\u56e0\u5e76\u4e0d\u771f\u6b63\u76f8\u5173\uff0c\u4f46\u91cd\u8981\u7684\u662f\u60a8\u8bb0\u4f4f<strong>0 \u7684\u9636\u4e58\u7b49\u4e8e 1<\/strong> \u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Lista-de-resultados-de-factoriales-de-numeros\"><\/span>\u6570\u5b57\u9636\u4e58\u7684\u7ed3\u679c\u5217\u8868<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e0b\u9762\u6211\u4eec\u5728\u8868\u683c\u4e2d\u603b\u7ed3\u4e86\u6700\u5e38\u7528\u6570\u5b57\u7684\u9636\u4e58\uff0c\u56e0\u6b64\u60a8\u4e0d\u5fc5\u624b\u52a8\u8ba1\u7b97\u5b83\u4eec\u3002 <\/p>\n<figure class=\"wp-block-table aligncenter is-style-stripes\">\n<table>\n<thead>\n<tr>\n<th class=\"has-text-align-center\" data-align=\"center\">\u53f7\u7801<\/th>\n<th class=\"has-text-align-center\" data-align=\"center\">\u6570\u5b57\u7684\u9636\u4e58<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">0<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 3<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 4<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 24<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 5<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 120<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 720<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 7<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 5,040<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 8<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 40,320<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 9<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 362,880<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\u5341<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">3,628,800<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\u5341\u4e00<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">39,916,800<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 12<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 479,001,600<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 13<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6,227,020,800<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 14<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 87 178 291 200<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\u5341\u4e94<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">1,307,674,368,000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 16<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 20,922,789,888,000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 17 \u53f7<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">355,687,428,096,000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 18<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 6,402,373,705,728,000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 19<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 121,645,100,408,832,000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\u4e8c\u5341<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">2,432,902,008 176,640,000<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\u4e94\u5341<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">3,041,409,320 \u00b7 <sup>10.64<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 100<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 9,332 621,544 \u00b7 <sup>10,157<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1,000<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 4,023,872,601\u00b7 <sup>10.2567<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 10,000<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2,846,259,681 \u00b7 <sup>10,35,659<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 100,000<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 2 824 229 408\u00b710 <sup>45 6573<\/sup><\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\"> 1,000,000<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\"> 8,263,931,688\u00b710 <sup>5,565,708<\/sup> <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Factorial-de-un-numero-con-la-calculadora\"><\/span>\u7528\u8ba1\u7b97\u5668\u8ba1\u7b97\u6570\u5b57\u7684\u9636\u4e58<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u60a8\u5728\u524d\u9762\u7684\u793a\u4f8b\u4e2d\u6240\u770b\u5230\u7684\uff0c\u4e24\u4e2a\u8fde\u7eed\u6570\u5b57\u7684\u9636\u4e58\u7ed3\u679c\u5448\u6307\u6570\u7ea7\u589e\u957f\uff0c\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u8981\u77e5\u9053\u5927\u6570\u7684\u9636\u4e58\u76f8\u5f53\u56f0\u96be\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u5411\u60a8\u5c55\u793a\u5982\u4f55\u4f7f\u7528\u8ba1\u7b97\u5668\u6c42\u6570\u5b57\u7684\u9636\u4e58\u3002<\/p>\n<p>\u79d1\u5b66\u8ba1\u7b97\u5668\u6709\u4e00\u4e2a\u5e26\u6709<em>x \u7b26\u53f7\u7684\u952e\uff01<\/em>\u6216<em>n\uff01<\/em>\u7528\u4e8e\u8ba1\u7b97\u6574\u6570\u7684\u9636\u4e58\u3002\u56e0\u6b64\uff0c\u8981\u786e\u5b9a\u9636\u4e58\u7684\u4ef7\u503c\uff0c\u60a8\u5fc5\u987b\u5728\u8ba1\u7b97\u5668\u4e0a\u6267\u884c\u4ee5\u4e0b\u5e8f\u5217\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c202f31b798e218ed65210a5eaff6293_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n! \\quad \\color{red} \\bm{\\longrightarrow} \\quad \\color{black} n\\rightarrow \\boxed{x!} \\rightarrow \\boxed{=}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"263\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u901a\u5e38\uff0cCASIO \u8ba1\u7b97\u5668\u6709<em><em>\u9636\u4e58\u952e x\uff01<\/em>\u6216<em>n\uff01<\/em><\/em> <em>x <sup>-1<\/sup><\/em>\u6309\u94ae\u4e0a\u65b9\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u8ba1\u7b97\u5668\u6c42\u89e3\u9636\u4e58\uff0c\u4ee5\u4fbf\u60a8\u53ef\u4ee5\u68c0\u67e5\u60a8\u662f\u5426\u77e5\u9053\u5982\u4f55\u6267\u884c\u6b64\u64cd\u4f5c\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u5c06\u8ba1\u7b97 9 \u7684\u9636\u4e58\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-797b93b341570c99b6ae23521134b3e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"9! \\quad \\color{red} \\bm{\\longrightarrow} \\quad \\color{black} 9\\rightarrow \\boxed{x!} \\rightarrow \\boxed{=} \\rightarrow 362880\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"340\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p>\u8981\u6c42 9 \u7684\u9636\u4e58\uff0c\u5fc5\u987b\u5148\u8f93\u5165\u6570\u5b57 9\uff0c\u7136\u540e\u6309 \u952e<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6e5326c9702600ee8b6727dc5e449b2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\boxed{x!}\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"27\" style=\"vertical-align: -6px;\"><\/p>\n<p>\u6700\u540e\uff0c\u6309\u7b49\u4e8e\u6309\u94ae\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8ba1\u7b97\u5668\u5e94\u8be5\u5411\u6211\u4eec\u663e\u793a\u7ed3\u679c 362,880\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aplicaciones-del-numero-factorial\"><\/span>\u9636\u4e58\u6570\u7684\u5e94\u7528<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6570\u5b57\u7684\u9636\u4e58\u51fd\u6570\u53ef\u80fd\u770b\u8d77\u6765\u662f\u4e00\u4e2a\u975e\u5e38\u7b80\u5355\u548c\u8352\u8c2c\u7684\u8fd0\u7b97\uff0c\u4f46\u5728\u9ad8\u7ea7\u4ee3\u6570\u4e2d\u5b83\u88ab\u5927\u91cf\u4f7f\u7528\u3002\u7136\u540e\u6211\u4eec\u5c06\u770b\u5230\u9636\u4e58\u7684\u4e3b\u8981\u7528\u9014\u3002<\/p>\n<p>\u9996\u5148\uff0c\u9636\u4e58\u662f\u8ba1\u7b97<a href=\"https:\/\/mathority.org\/cn\/\u7ec4\u5408\u6570\u4e8c\u9879\u5f0f\u7cfb\u6570\u6027\u8d28\/\"><strong><span style=\"text-decoration: underline;\">\u7ec4\u5408\u6570\u7684<\/span><\/strong><\/a>\u57fa\u672c\u8fd0\u7b97\uff0c\u662f\u4e00\u79cd\u66f4\u7279\u6b8a\u7684\u8fd0\u7b97\u3002\u5982\u679c\u60a8\u4e0d\u77e5\u9053\u7ec4\u5408\u6570\u662f\u4ec0\u4e48\uff0c\u60a8\u53ef\u4ee5\u5728\u6b64\u94fe\u63a5\u4e2d\u67e5\u770b\u5b83\u7684\u7ec4\u6210\u4ee5\u53ca\u5b83\u7684\u8ba1\u7b97\u65b9\u5f0f\uff0c\u60a8\u53ef\u4ee5\u5728\u5176\u4e2d\u627e\u5230\u793a\u4f8b\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u53ca\u5176\u5c5e\u6027\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u5b83\u7684\u7528\u9014\uff0c\u56e0\u4e3a\u5b83\u6709\u8bb8\u591a\u5b9e\u9645\u5e94\u7528\u7a0b\u5e8f\u3002<\/p>\n<p>\u9636\u4e58\u8fd8\u5728\u6570\u5b66\u4e2d\u7528\u4e8e\u786e\u5b9a\u51fd\u6570\u7684\u6cf0\u52d2\u591a\u9879\u5f0f\u3002<\/p>\n<p>\u540c\u6837\uff0c\u9636\u4e58\u7528\u4e8e\u89e3\u51b3\u67d0\u4e9b\u7ec4\u5408\u95ee\u9898\uff0c\u7279\u522b\u662f\u8ba1\u7b97\u7ec4\u5408\u548c\u6392\u5217\u3002\u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u8bf4\uff0c\u9636\u4e58\u4e5f\u7ecf\u5e38\u7528\u4e8e\u4f7f\u7528\u7ec4\u5408\u6570\u5b66\u6765\u8ba1\u7b97\u6982\u7387\u3002<\/p>\n<p> n \u4e2a\u5143\u7d20\u7684\u6392\u5217\u5bf9\u5e94\u4e8e\u53ef\u4ee5\u7528\u8fd9\u4e9b\u5143\u7d20\u8fdb\u884c\u7684\u6bcf\u79cd\u4e0d\u540c\u6392\u5217\u3002\u56e0\u6b64\uff0c\u4e3a\u4e86\u8ba1\u7b97\u6392\u5217\uff0c\u9700\u8981\u4f7f\u7528\u9636\u4e58\u3002\u4f8b\u5982\uff0c\u5982\u679c\u5728\u4e00\u4e2a\u95ee\u9898\u4e2d\u60a8\u60f3\u8981\u627e\u5230 7 \u4e2a\u5bf9\u8c61\u53ef\u4ee5\u6392\u5217\u7684\u53ef\u80fd\u6027\u6570\u91cf\uff0c\u5219\u5fc5\u987b\u8ba1\u7b97 7 \u7684\u9636\u4e58\u3002<\/p>\n<p>\u73b0\u5728\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff1a<\/p>\n<ul>\n<li>\u6211\u4eec\u6709 5 \u53cc\u4e0d\u540c\u7684\u978b\u5b50\uff0c\u6211\u4eec\u6709\u591a\u5c11\u79cd\u6392\u5217\u65b9\u5f0f\uff1f<\/li>\n<\/ul>\n<p>\u5728\u8fd9\u4e2a\u7ec3\u4e60\u4e2d\uff0c\u6211\u4eec\u5fc5\u987b\u8003\u8651\u5230\u6211\u4eec\u653e\u7f6e\u8fd9 5 \u53cc\u978b\u7684\u987a\u5e8f\uff0c\u627e\u51fa\u6240\u6709\u53ef\u80fd\u7684\u7ec4\u5408\u65b9\u5f0f\u3002\u56e0\u6b64\uff0c\u8981\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u60a8\u53ea\u9700\u8ba1\u7b97 5 \u7684\u9636\u4e58\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6725f02a218ddc6ac88f42df99e13261_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5! = 1\\cdot 2 \\cdot 3\\cdot 4\\cdot 5 =120\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"184\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c5\u53cc\u978b\u53ef\u4ee5\u6709120\u79cd\u4e0d\u540c\u7684\u6446\u653e\u65b9\u5f0f\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-del-numero-factorial\"><\/span>\u9636\u4e58\u6570\u7684\u6027\u8d28<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u9636\u4e58\u6570\u5177\u6709\u4ee5\u4e0b\u7279\u70b9\uff1a<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u4e3a\u4e24\u4e2a\u6b63\u6574\u6570<em>n<\/em>\u548c<em>m<\/em>\u4e14<em>n<\/em>\u5927\u4e8e<em>m<\/em> \uff0c\u5219\u663e\u7136<em>n<\/em>\u7684\u9636\u4e58\u503c\u5927\u4e8e<em>m<\/em>\u7684\u9636\u4e58\u503c\u3002<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e858d82412bf78abe42397373dc67e5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n>m \\quad \\longrightarrow \\quad n! > m!&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;15&#8243; width=&#8221;183&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u4e00\u4e2a\u6570\u7684\u9636\u4e58\u53ef\u4ee5\u88ab\u9636\u4e58\u5206\u89e3\uff0c\u4f7f\u5f97\u5176\u4e2d\u4e00\u4e2a\u56e0\u5b50\u662f\u8f83\u5c0f\u6570\u7684\u9636\u4e58\u3002<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-37ca3a1bea020ccbff019c2e1766be93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n>m \\quad \\longrightarrow \\quad n!= n\\cdot (n-1) \\cdots (m+1)\\cdot m!&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;361&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c6 \u5927\u4e8e 4\uff0c\u56e0\u6b64 6 \u7684\u9636\u4e58\u8868\u8fbe\u5f0f\u53ef\u4ee5\u7b80\u5316\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0ca24a5de3e3cad7df5fc66d694e6eee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6! = 6 \\cdot 5 \\cdot 4!\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul style=\"color:#ff5733; font-weight: bold;\">\n<li><span style=\"color:#000000;font-weight: normal;\">\u4ee5\u4e0b\u4ee3\u6570\u8868\u8fbe\u5f0f\u5bf9\u4e8e\u4efb\u4f55\u6570\u5b57\u7684\u9636\u4e58\u90fd\u6709\u6548\uff0c\u4f46 1 \u7684\u9636\u4e58\u9664\u5916\uff1a<\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35dd01cda41e2b84fbf524ff6632b4f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle n!< \\left( \\frac{n+1}{2} \\right)^n\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"118\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Factorial-de-un-numero-negativo-o-decimal\"><\/span>\u8d1f\u6570\u6216\u5c0f\u6570\u7684\u9636\u4e58<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6211\u4eec\u521a\u521a\u770b\u5230\u4e86\u5982\u4f55\u6c42\u6b63\u6574\u6570\u7684\u9636\u4e58\u503c\uff0c\u4f46\u662f\u2026\u2026\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u8d1f\u6570\u6216\u5c0f\u6570\u7684\u9636\u4e58\u5417\uff1f\u7b54\u6848\u662f\u80af\u5b9a\u7684\uff0c\u4f46\u9700\u8981\u5148\u8fdb\u7684\u6570\u5b66\u77e5\u8bc6\u3002<\/p>\n<p>\u8d1f\u6570\u548c\u5c0f\u6570\u7684\u9636\u4e58\u662f\u4f7f\u7528\u79f0\u4e3a\u6b27\u62c9\u201c\u4f3d\u739b\u51fd\u6570\u201d\u7684\u7279\u6b8a\u51fd\u6570\u8ba1\u7b97\u7684\uff0c\u8be5\u51fd\u6570\u7531\u4ee5\u4e0b\u79ef\u5206\u5b9a\u4e49\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20553bef4090def5334022fbbd8f646b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\Gamma(z)=\\int_0^\\infty t^{z-1} e^{-t}\\, \\mathrm{d}t\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"168\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4efb\u4f55\u7c7b\u578b\u7684\u9636\u4e58\u90fd\u53ef\u4ee5\u4f7f\u7528 Gamma \u51fd\u6570\u6c42\u89e3\uff0c\u56e0\u4e3a\u4ee5\u4e0b\u65b9\u7a0b\u59cb\u7ec8\u4e3a\u771f\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d336cefb8a14d587ad508fcde7c55914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n! = \\Gamma(n+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u4f8b\u5982\uff0c\u8981\u627e\u5230 0.5 \u7684\u9636\u4e58\uff0c\u6211\u4eec\u5fc5\u987b\u627e\u5230<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74cf80cb3a1094ad541acd2fadab6c93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Gamma(1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"50\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u56e0\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b2359c9eadbef6aad92eb84450a4165_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,5! = \\Gamma(0,5+1) =\\Gamma(1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\">\u79ef\u5206\u7684\u89e3\u5c06\u5bf9\u5e94\u4e8e 0.5 \u7684\u9636\u4e58\u3002<\/p>\n<p>\u663e\u7136\uff0c\u6c42\u89e3 Gamma \u51fd\u6570\u7684\u79ef\u5206\u5e76\u4e0d\u5bb9\u6613\uff0c\u6211\u4eec\u5728\u672c\u6587\u4e2d\u4e0d\u4f1a\u6559\u6388\u5b83\uff0c\u56e0\u4e3a\u8bb8\u591a\u6570\u5b66\u6982\u5ff5\u5fc5\u987b\u4e8b\u5148\u89e3\u91ca\u3002\u4f46\u6211\u4eec\u60f3\u8ba9\u60a8\u77e5\u9053\uff0c\u53ef\u4ee5\u8ba1\u7b97\u8d1f\u6570\u6216\u5c0f\u6570\u7684\u9636\u4e58\u3002<\/p>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u4f5c\u4e3a\u4e00\u4e2a\u4f8b\u5b50\uff0c\u6211\u4eec\u8ba1\u7b97\u4e86\u4e00\u4e9b\u8d1f\u7684\u9636\u4e58\u548c\u5c0f\u6570\u503c\uff1a <\/p>\n<figure class=\"wp-block-table aligncenter is-style-stripes\">\n<table>\n<tbody>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7ad27047f682b1254c792b678fc5fdf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\underline{\\bm{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: -3px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b827a8ed6060949fe26a6587d7f0967a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\underline{\\bm{n!}}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1d9404653c812c40471f884311057d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{1}{2}\\right)!\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"40\" style=\"vertical-align: -17px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23d859aa265b7e809f660f3044c24290_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{1}{2}\\sqrt{\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"37\" style=\"vertical-align: -12px;\"><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a19589a09d32e0a6528c6504a6011606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(-\\frac{1}{2}\\right)!\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"54\" style=\"vertical-align: -17px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bdb20bafedd2cc451408e573c7e9d3c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\sqrt{\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"25\" style=\"vertical-align: -3px;\"><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fb86f24adb23da02e1f18f7d06c4e851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{3}{2}\\right)!\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"40\" style=\"vertical-align: -17px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cbc4e85460f947ab1d92294e3847264e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{3}{4}\\sqrt{\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"37\" style=\"vertical-align: -12px;\"><\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-973e06c4da8ee3607e1e8f94a7a7bf4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\frac{5}{2}\\right)!\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"40\" style=\"vertical-align: -17px;\"><\/p>\n<\/td>\n<td class=\"has-text-align-center\" data-align=\"center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c675261e5e335903926dc229dae84d9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\frac{15}{8}\\sqrt{\\pi}\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"45\" style=\"vertical-align: -12px;\"><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u9875\u89e3\u91ca\u4ec0\u4e48\u662f\u6570\u5b57\u7684\u9636\u4e58\u53ca\u5176\u8ba1\u7b97\u65b9\u6cd5\u3002\u6b64\u5916\uff0c\u8fd8\u63d0\u4f9b\u4e86\u51e0\u4e2a\u793a\u4f8b\u548c\u4e00\u4e2a\u5305\u542b\u6700\u5e38\u7528\u9636\u4e58\u503c\u7684\u8868\u683c\u3002\u5b83\u8fd8\u6559\u6388\u5982\u4f55\u4f7f\u7528\u8ba1\u7b97 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" 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