{"id":570990,"date":"2026-07-27T15:12:50","date_gmt":"2026-07-27T08:12:50","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=570990"},"modified":"2026-07-27T15:12:50","modified_gmt":"2026-07-27T08:12:50","slug":"giai-thua-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/giai-thua-la-gi\/","title":{"rendered":"Giai th\u1eeba l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c n!, b\u1ea3ng gi\u00e1 tr\u1ecb v\u00e0 \u1ee9ng d\u1ee5ng"},"content":{"rendered":"<p><strong>Giai th\u1eeba c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean n, k\u00fd hi\u1ec7u n!, l\u00e0 t\u00edch c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 nguy\u00ean d\u01b0\u01a1ng t\u1eeb 1 \u0111\u1ebfn n: n! = 1 \u00d7 2 \u00d7 3 \u00d7 \u2026 \u00d7 n.<\/strong> \u0110\u1eb7c bi\u1ec7t, ng\u01b0\u1eddi ta quy \u01b0\u1edbc 0! = 1. \u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m n\u1ec1n t\u1ea3ng c\u1ee7a to\u00e1n t\u1ed5 h\u1ee3p v\u00e0 x\u00e1c su\u1ea5t, xu\u1ea5t hi\u1ec7n th\u01b0\u1eddng xuy\u00ean trong c\u00e1c b\u00e0i to\u00e1n \u0111\u1ebfm s\u1ed1 c\u00e1ch s\u1eafp x\u1ebfp, ch\u1ecdn l\u1ef1a. N\u1ebfu b\u1ea1n t\u1eebng b\u1ed1i r\u1ed1i v\u00ec sao 0! l\u1ea1i b\u1eb1ng 1 hay l\u00e0m th\u1ebf n\u00e0o \u0111\u1ec3 r\u00fat g\u1ecdn m\u1ed9t bi\u1ec3u th\u1ee9c ch\u1ee9a giai th\u1eeba kh\u1ed5ng l\u1ed3 m\u00e0 kh\u00f4ng c\u1ea7n b\u1ea5m m\u00e1y t\u00ednh, b\u00e0i vi\u1ebft d\u01b0\u1edbi \u0111\u00e2y s\u1ebd gi\u00fap b\u1ea1n hi\u1ec3u r\u00f5 \u0111\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c, b\u1ea3ng gi\u00e1 tr\u1ecb, t\u00ednh ch\u1ea5t, \u1ee9ng d\u1ee5ng v\u00e0 c\u1ea3 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft.<\/p>\n<h2>Giai th\u1eeba l\u00e0 g\u00ec?<\/h2>\n<p>Giai th\u1eeba c\u1ee7a s\u1ed1 t\u1ef1 nhi\u00ean n l\u00e0 t\u00edch c\u1ee7a n s\u1ed1 nguy\u00ean d\u01b0\u01a1ng \u0111\u1ea7u ti\u00ean, \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u b\u1eb1ng m\u1ed9t d\u1ea5u ch\u1ea5m than \u0111\u1eb7t sau s\u1ed1: n!. N\u00f3i c\u00e1ch kh\u00e1c, \u0111\u1ec3 t\u00ednh giai th\u1eeba c\u1ee7a n, b\u1ea1n ch\u1ec9 vi\u1ec7c nh\u00e2n l\u1ea7n l\u01b0\u1ee3t t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 nguy\u00ean d\u01b0\u01a1ng t\u1eeb 1 cho \u0111\u1ebfn n.<\/p>\n<p>V\u00ed d\u1ee5 minh h\u1ecda:<\/p>\n<ul>\n<li>4! = 1 \u00d7 2 \u00d7 3 \u00d7 4 = 24.<\/li>\n<li>5! = 1 \u00d7 2 \u00d7 3 \u00d7 4 \u00d7 5 = 120.<\/li>\n<li>3! = 1 \u00d7 2 \u00d7 3 = 6.<\/li>\n<\/ul>\n<p>Giai th\u1eeba ch\u1ec9 \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a cho s\u1ed1 t\u1ef1 nhi\u00ean (s\u1ed1 nguy\u00ean kh\u00f4ng \u00e2m). V\u1edbi c\u00e1c s\u1ed1 \u00e2m ho\u1eb7c s\u1ed1 th\u1eadp ph\u00e2n, giai th\u1eeba th\u00f4ng th\u01b0\u1eddng kh\u00f4ng t\u1ed3n t\u1ea1i (ch\u00fang \u0111\u01b0\u1ee3c m\u1edf r\u1ed9ng b\u1eb1ng h\u00e0m Gamma \u1edf b\u1eadc h\u1ecdc cao h\u01a1n, kh\u00f4ng thu\u1ed9c ph\u1ea1m vi ch\u01b0\u01a1ng tr\u00ecnh ph\u1ed5 th\u00f4ng).<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-571003\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-3.jpg\" alt=\"giai-thua-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c v\u00e0 quy \u01b0\u1edbc c\u1ee7a giai th\u1eeba<\/h2>\n<p>C\u00f4ng th\u1ee9c t\u1ed5ng qu\u00e1t c\u1ee7a giai th\u1eeba \u0111\u01b0\u1ee3c vi\u1ebft g\u1ecdn nh\u01b0 sau:<\/p>\n<p><strong>n! = 1 \u00d7 2 \u00d7 3 \u00d7 \u2026 \u00d7 (n \u2212 1) \u00d7 n<\/strong><\/p>\n<p>\u0110i k\u00e8m c\u00f4ng th\u1ee9c n\u00e0y l\u00e0 hai quy \u01b0\u1edbc quan tr\u1ecdng m\u00e0 b\u1ea1n c\u1ea7n ghi nh\u1edb:<\/p>\n<ul>\n<li><strong>0! = 1.<\/strong> \u0110\u00e2y l\u00e0 quy \u01b0\u1edbc to\u00e1n h\u1ecdc, gi\u00fap c\u00e1c c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p v\u00e0 khai tri\u1ec3n nh\u1ecb th\u1ee9c lu\u00f4n \u0111\u00fang trong m\u1ecdi tr\u01b0\u1eddng h\u1ee3p. C\u00f3 th\u1ec3 hi\u1ec3u \u0111\u01a1n gi\u1ea3n: ch\u1ec9 c\u00f3 \u0111\u00fang 1 c\u00e1ch s\u1eafp x\u1ebfp m\u1ed9t t\u1eadp r\u1ed7ng (kh\u00f4ng s\u1eafp x\u1ebfp g\u00ec c\u1ea3).<\/li>\n<li><strong>1! = 1.<\/strong> Ch\u1ec9 c\u00f3 duy nh\u1ea5t 1 c\u00e1ch s\u1eafp x\u1ebfp m\u1ed9t ph\u1ea7n t\u1eed.<\/li>\n<li>Giai th\u1eeba kh\u00f4ng \u0111\u1ecbnh ngh\u0129a cho s\u1ed1 \u00e2m.<\/li>\n<\/ul>\n<h2>C\u00f4ng th\u1ee9c truy h\u1ed3i v\u00e0 c\u00e1ch t\u00ednh giai th\u1eeba<\/h2>\n<p>M\u1ed9t trong nh\u1eefng t\u00ednh ch\u1ea5t \u0111\u1eb9p nh\u1ea5t c\u1ee7a giai th\u1eeba l\u00e0 c\u00f4ng th\u1ee9c truy h\u1ed3i (\u0111\u1ec7 quy):<\/p>\n<p><strong>n! = n \u00d7 (n \u2212 1)!<\/strong><\/p>\n<p>C\u00f4ng th\u1ee9c n\u00e0y n\u00f3i r\u1eb1ng giai th\u1eeba c\u1ee7a n b\u1eb1ng n nh\u00e2n v\u1edbi giai th\u1eeba c\u1ee7a s\u1ed1 li\u1ec1n tr\u01b0\u1edbc n\u00f3. V\u00ed d\u1ee5: 6! = 6 \u00d7 5! = 6 \u00d7 120 = 720. Nh\u1edd v\u1eady, n\u1ebfu \u0111\u00e3 bi\u1ebft gi\u00e1 tr\u1ecb c\u1ee7a m\u1ed9t giai th\u1eeba nh\u1ecf, b\u1ea1n c\u00f3 th\u1ec3 suy ra giai th\u1eeba l\u1edbn h\u01a1n m\u00e0 kh\u00f4ng c\u1ea7n nh\u00e2n l\u1ea1i t\u1eeb \u0111\u1ea7u.<\/p>\n<p>M\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t c\u1ea7n nh\u1edb:<\/p>\n<ul>\n<li>Giai th\u1eeba lu\u00f4n l\u00e0 s\u1ed1 nguy\u00ean d\u01b0\u01a1ng.<\/li>\n<li>Giai th\u1eeba t\u0103ng c\u1ef1c nhanh: t\u1eeb 10! \u0111\u00e3 l\u00ean t\u1edbi h\u01a1n 3,6 tri\u1ec7u.<\/li>\n<li>C\u00f4ng th\u1ee9c truy h\u1ed3i gi\u00fap r\u00fat g\u1ecdn nhanh bi\u1ec3u th\u1ee9c ch\u1ee9a giai th\u1eeba, v\u00ed d\u1ee5 8!\/6! = 8 \u00d7 7 = 56.<\/li>\n<\/ul>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-571005\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-2.jpg\" alt=\"giai-thua-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>B\u1ea3ng gi\u00e1 tr\u1ecb giai th\u1eeba t\u1eeb 0! \u0111\u1ebfn 10!<\/h2>\n<p>B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y li\u1ec7t k\u00ea gi\u00e1 tr\u1ecb giai th\u1eeba c\u1ee7a c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 0 \u0111\u1ebfn 10 \u0111\u1ec3 b\u1ea1n tra c\u1ee9u nhanh khi l\u00e0m b\u00e0i t\u1eadp.<\/p>\n<table>\n<thead>\n<tr>\n<th>n<\/th>\n<th>n! (giai th\u1eeba)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>1<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>2<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>6<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>24<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>120<\/td>\n<\/tr>\n<tr>\n<td>6<\/td>\n<td>720<\/td>\n<\/tr>\n<tr>\n<td>7<\/td>\n<td>5.040<\/td>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>40.320<\/td>\n<\/tr>\n<tr>\n<td>9<\/td>\n<td>362.880<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>3.628.800<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>C\u00f3 th\u1ec3 th\u1ea5y gi\u00e1 tr\u1ecb giai th\u1eeba t\u0103ng l\u00ean r\u1ea5t nhanh. \u0110\u00e2y c\u0169ng l\u00e0 l\u00fd do trong l\u1eadp tr\u00ecnh, ng\u01b0\u1eddi ta ph\u1ea3i ch\u00fa \u00fd \u0111\u1ebfn gi\u1edbi h\u1ea1n ki\u1ec3u d\u1eef li\u1ec7u khi t\u00ednh giai th\u1eeba c\u1ee7a nh\u1eefng s\u1ed1 l\u1edbn.<\/p>\n<h2>\u1ee8ng d\u1ee5ng c\u1ee7a giai th\u1eeba trong to\u00e1n t\u1ed5 h\u1ee3p<\/h2>\n<p>Giai th\u1eeba l\u00e0 c\u00f4ng c\u1ee5 c\u1ed1t l\u00f5i \u0111\u1ec3 \u0111\u1ebfm s\u1ed1 c\u00e1ch s\u1eafp x\u1ebfp v\u00e0 ch\u1ecdn l\u1ef1a, xu\u1ea5t hi\u1ec7n trong ba c\u00f4ng th\u1ee9c \u0111\u1ebfm c\u01a1 b\u1ea3n:<\/p>\n<ul>\n<li><strong>Ho\u00e1n v\u1ecb:<\/strong> s\u1ed1 c\u00e1ch s\u1eafp x\u1ebfp th\u1ee9 t\u1ef1 n ph\u1ea7n t\u1eed kh\u00e1c nhau l\u00e0 P<sub>n<\/sub> = n!.<\/li>\n<li><strong>Ch\u1ec9nh h\u1ee3p:<\/strong> s\u1ed1 c\u00e1ch ch\u1ecdn v\u00e0 s\u1eafp x\u1ebfp k ph\u1ea7n t\u1eed t\u1eeb n ph\u1ea7n t\u1eed l\u00e0 A(n, k) = n! \/ (n \u2212 k)!.<\/li>\n<li><strong>T\u1ed5 h\u1ee3p:<\/strong> s\u1ed1 c\u00e1ch ch\u1ecdn k ph\u1ea7n t\u1eed t\u1eeb n ph\u1ea7n t\u1eed (kh\u00f4ng quan t\u00e2m th\u1ee9 t\u1ef1) l\u00e0 C(n, k) = n! \/ [k! \u00d7 (n \u2212 k)!].<\/li>\n<\/ul>\n<p>Ngo\u00e0i ra, giai th\u1eeba c\u00f2n xu\u1ea5t hi\u1ec7n trong khai tri\u1ec3n nh\u1ecb th\u1ee9c Newton v\u00e0 nhi\u1ec1u b\u00e0i to\u00e1n x\u00e1c su\u1ea5t. N\u1ebfu b\u1ea1n th\u00edch kh\u00e1m ph\u00e1 c\u00e1c d\u00e3y s\u1ed1 v\u00e0 quy lu\u1eadt to\u00e1n h\u1ecdc th\u00fa v\u1ecb kh\u00e1c, c\u00f3 th\u1ec3 tham kh\u1ea3o th\u00eam b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/day-fibonacci-la-gi\/\">d\u00e3y Fibonacci l\u00e0 g\u00ec<\/a> ho\u1eb7c kh\u00e1i ni\u1ec7m <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/so-nguyen-to-cung-nhau\/\">s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau<\/a>.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-571006\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-4.jpg\" alt=\"giai-thua-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1ch r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c ch\u1ee9a giai th\u1eeba<\/h2>\n<p>Nh\u1edd c\u00f4ng th\u1ee9c truy h\u1ed3i, b\u1ea1n c\u00f3 th\u1ec3 r\u00fat g\u1ecdn nhanh c\u00e1c bi\u1ec3u th\u1ee9c ch\u1ee9a giai th\u1eeba m\u00e0 kh\u00f4ng c\u1ea7n t\u00ednh gi\u00e1 tr\u1ecb \u0111\u1ea7y \u0111\u1ee7 (v\u1ed1n r\u1ea5t l\u1edbn). Nguy\u00ean t\u1eafc l\u00e0: vi\u1ebft giai th\u1eeba l\u1edbn theo giai th\u1eeba nh\u1ecf r\u1ed3i tri\u1ec7t ti\u00eau ph\u1ea7n chung.<\/p>\n<p>V\u00ed d\u1ee5:<\/p>\n<ul>\n<li>10!\/8! = (10 \u00d7 9 \u00d7 8!)\/8! = 10 \u00d7 9 = 90.<\/li>\n<li>(n + 1)!\/n! = n + 1.<\/li>\n<li>7!\/(5! \u00d7 2!) = (7 \u00d7 6)\/2 = 21.<\/li>\n<\/ul>\n<p>K\u1ef9 thu\u1eadt n\u00e0y r\u1ea5t h\u1eefu \u00edch khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh, b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh ch\u1ee9a giai th\u1eeba ho\u1eb7c r\u00fat g\u1ecdn c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p trong c\u00e1c b\u00e0i to\u00e1n \u0111\u1ebfm.<\/p>\n<h2>Giai th\u1eeba trong l\u1eadp tr\u00ecnh<\/h2>\n<p>T\u00ednh giai th\u1eeba l\u00e0 b\u00e0i to\u00e1n kinh \u0111i\u1ec3n khi m\u1edbi h\u1ecdc l\u1eadp tr\u00ecnh, th\u01b0\u1eddng \u0111\u01b0\u1ee3c c\u00e0i \u0111\u1eb7t b\u1eb1ng hai c\u00e1ch. C\u00e1ch th\u1ee9 nh\u1ea5t l\u00e0 d\u00f9ng v\u00f2ng l\u1eb7p: kh\u1edfi t\u1ea1o k\u1ebft qu\u1ea3 b\u1eb1ng 1 r\u1ed3i nh\u00e2n d\u1ed3n l\u1ea7n l\u01b0\u1ee3t t\u1eeb 1 \u0111\u1ebfn n. C\u00e1ch th\u1ee9 hai l\u00e0 d\u00f9ng \u0111\u1ec7 quy, d\u1ef1a tr\u1ef1c ti\u1ebfp tr\u00ean c\u00f4ng th\u1ee9c truy h\u1ed3i n! = n \u00d7 (n \u2212 1)! v\u1edbi \u0111i\u1ec1u ki\u1ec7n d\u1eebng l\u00e0 0! = 1.<\/p>\n<p>\u0110i\u1ec3m c\u1ea7n l\u01b0u \u00fd: v\u00ec giai th\u1eeba t\u0103ng r\u1ea5t nhanh n\u00ean ch\u1ec9 kho\u1ea3ng 21! \u0111\u00e3 v\u01b0\u1ee3t ph\u1ea1m vi c\u1ee7a s\u1ed1 nguy\u00ean 64 bit th\u00f4ng th\u01b0\u1eddng. V\u1edbi nh\u1eefng s\u1ed1 l\u1edbn, l\u1eadp tr\u00ecnh vi\u00ean ph\u1ea3i d\u00f9ng ki\u1ec3u s\u1ed1 nguy\u00ean l\u1edbn (big integer) ho\u1eb7c th\u01b0 vi\u1ec7n chuy\u00ean d\u1ee5ng \u0111\u1ec3 tr\u00e1nh tr\u00e0n s\u1ed1.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-571004\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-1.jpg\" alt=\"giai-thua-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/07\/giai-thua-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<ul>\n<li><strong>B\u00e0i 1:<\/strong> T\u00ednh 5! v\u00e0 6!. <em>L\u1eddi gi\u1ea3i:<\/em> 5! = 120; 6! = 6 \u00d7 120 = 720.<\/li>\n<li><strong>B\u00e0i 2:<\/strong> R\u00fat g\u1ecdn 9!\/7!. <em>L\u1eddi gi\u1ea3i:<\/em> = 9 \u00d7 8 = 72.<\/li>\n<li><strong>B\u00e0i 3:<\/strong> C\u00f3 bao nhi\u00eau c\u00e1ch s\u1eafp x\u1ebfp 4 h\u1ecdc sinh v\u00e0o 4 ch\u1ed7 ng\u1ed3i? <em>L\u1eddi gi\u1ea3i:<\/em> P\u2084 = 4! = 24 c\u00e1ch.<\/li>\n<li><strong>B\u00e0i 4:<\/strong> T\u00ednh C(5, 2). <em>L\u1eddi gi\u1ea3i:<\/em> = 5!\/(2! \u00d7 3!) = 120\/(2 \u00d7 6) = 10.<\/li>\n<li><strong>B\u00e0i 5:<\/strong> T\u00ednh A(6, 2). <em>L\u1eddi gi\u1ea3i:<\/em> = 6!\/(6 \u2212 2)! = 6!\/4! = 6 \u00d7 5 = 30.<\/li>\n<li><strong>B\u00e0i 6 (tr\u1eafc nghi\u1ec7m):<\/strong> Gi\u00e1 tr\u1ecb c\u1ee7a 0! l\u00e0 bao nhi\u00eau? A. 0 B. 1 C. Kh\u00f4ng x\u00e1c \u0111\u1ecbnh D. V\u00f4 c\u00f9ng. <em>\u0110\u00e1p \u00e1n:<\/em> B.<\/li>\n<\/ul>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p<\/h2>\n<h3>0! b\u1eb1ng bao nhi\u00eau?<\/h3>\n<p>0! b\u1eb1ng 1, theo quy \u01b0\u1edbc to\u00e1n h\u1ecdc. Quy \u01b0\u1edbc n\u00e0y gi\u00fap c\u00e1c c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p v\u00e0 khai tri\u1ec3n nh\u1ecb th\u1ee9c lu\u00f4n \u0111\u00fang.<\/p>\n<h3>C\u00f4ng th\u1ee9c truy h\u1ed3i c\u1ee7a giai th\u1eeba l\u00e0 g\u00ec?<\/h3>\n<p>C\u00f4ng th\u1ee9c truy h\u1ed3i l\u00e0 n! = n \u00d7 (n \u2212 1)!, ngh\u0129a l\u00e0 giai th\u1eeba c\u1ee7a n b\u1eb1ng n nh\u00e2n v\u1edbi giai th\u1eeba c\u1ee7a s\u1ed1 li\u1ec1n tr\u01b0\u1edbc.<\/p>\n<h3>5! b\u1eb1ng bao nhi\u00eau?<\/h3>\n<p>5! = 1 \u00d7 2 \u00d7 3 \u00d7 4 \u00d7 5 = 120.<\/p>\n<h3>Giai th\u1eeba d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?<\/h3>\n<p>Giai th\u1eeba \u0111\u01b0\u1ee3c d\u00f9ng trong c\u00f4ng th\u1ee9c ho\u00e1n v\u1ecb, ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p, khai tri\u1ec3n nh\u1ecb th\u1ee9c v\u00e0 c\u00e1c b\u00e0i to\u00e1n \u0111\u1ebfm, x\u00e1c su\u1ea5t.<\/p>\n<h3>Giai th\u1eeba c\u1ee7a s\u1ed1 \u00e2m c\u00f3 t\u1ed3n t\u1ea1i kh\u00f4ng?<\/h3>\n<p>Kh\u00f4ng. Giai th\u1eeba th\u00f4ng th\u01b0\u1eddng ch\u1ec9 \u0111\u1ecbnh ngh\u0129a cho s\u1ed1 t\u1ef1 nhi\u00ean (s\u1ed1 nguy\u00ean kh\u00f4ng \u00e2m).<\/p>\n<h3>V\u00ec sao giai th\u1eeba t\u0103ng nhanh nh\u01b0 v\u1eady?<\/h3>\n<p>V\u00ec m\u1ed7i b\u01b0\u1edbc ta nh\u00e2n th\u00eam m\u1ed9t s\u1ed1 l\u1edbn h\u01a1n, n\u00ean gi\u00e1 tr\u1ecb t\u0103ng theo c\u1ea5p s\u1ed1 nh\u00e2n d\u1ed3n; ch\u1ec9 \u0111\u1ebfn 10! \u0111\u00e3 h\u01a1n 3,6 tri\u1ec7u.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>T\u00f3m l\u1ea1i, <strong>giai th\u1eeba n! l\u00e0 t\u00edch c\u00e1c s\u1ed1 nguy\u00ean d\u01b0\u01a1ng t\u1eeb 1 \u0111\u1ebfn n, v\u1edbi quy \u01b0\u1edbc 0! = 1 v\u00e0 c\u00f4ng th\u1ee9c truy h\u1ed3i n! = n \u00d7 (n \u2212 1)!<\/strong>. \u0110\u00e2y l\u00e0 c\u00f4ng c\u1ee5 c\u1ed1t l\u00f5i c\u1ee7a to\u00e1n t\u1ed5 h\u1ee3p, x\u00e1c su\u1ea5t v\u00e0 c\u1ea3 l\u1eadp tr\u00ecnh. N\u1eafm v\u1eefng \u0111\u1ecbnh ngh\u0129a, b\u1ea3ng gi\u00e1 tr\u1ecb c\u00f9ng c\u00e1ch r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c s\u1ebd gi\u00fap b\u1ea1n gi\u1ea3i nhanh c\u00e1c b\u00e0i to\u00e1n \u0111\u1ebfm. B\u1ea1n h\u00e3y luy\u1ec7n th\u00eam v\u1edbi c\u00e1c b\u00e0i t\u1eadp \u1edf tr\u00ean \u0111\u1ec3 ghi nh\u1edb c\u00f4ng th\u1ee9c th\u1eadt ch\u1eafc nh\u00e9.<br \/>\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"0! b\u1eb1ng bao nhi\u00eau?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"0! b\u1eb1ng 1, theo quy \u01b0\u1edbc to\u00e1n h\u1ecdc. Quy \u01b0\u1edbc n\u00e0y gi\u00fap c\u00e1c c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p v\u00e0 khai tri\u1ec3n nh\u1ecb th\u1ee9c lu\u00f4n \u0111\u00fang.\"}},{\"@type\":\"Question\",\"name\":\"C\u00f4ng th\u1ee9c truy h\u1ed3i c\u1ee7a giai th\u1eeba l\u00e0 g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"C\u00f4ng th\u1ee9c truy h\u1ed3i l\u00e0 n! = n \u00d7 (n \u2212 1)!, ngh\u0129a l\u00e0 giai th\u1eeba c\u1ee7a n b\u1eb1ng n nh\u00e2n v\u1edbi giai th\u1eeba c\u1ee7a s\u1ed1 li\u1ec1n tr\u01b0\u1edbc.\"}},{\"@type\":\"Question\",\"name\":\"5! b\u1eb1ng bao nhi\u00eau?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"5! = 1 \u00d7 2 \u00d7 3 \u00d7 4 \u00d7 5 = 120.\"}},{\"@type\":\"Question\",\"name\":\"Giai th\u1eeba d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Giai th\u1eeba \u0111\u01b0\u1ee3c d\u00f9ng trong c\u00f4ng th\u1ee9c ho\u00e1n v\u1ecb, ch\u1ec9nh h\u1ee3p, t\u1ed5 h\u1ee3p, khai tri\u1ec3n nh\u1ecb th\u1ee9c v\u00e0 c\u00e1c b\u00e0i to\u00e1n \u0111\u1ebfm, x\u00e1c su\u1ea5t.\"}},{\"@type\":\"Question\",\"name\":\"Giai th\u1eeba c\u1ee7a s\u1ed1 \u00e2m c\u00f3 t\u1ed3n t\u1ea1i kh\u00f4ng?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Kh\u00f4ng. Giai th\u1eeba th\u00f4ng th\u01b0\u1eddng ch\u1ec9 \u0111\u1ecbnh ngh\u0129a cho s\u1ed1 t\u1ef1 nhi\u00ean (s\u1ed1 nguy\u00ean kh\u00f4ng \u00e2m).\"}},{\"@type\":\"Question\",\"name\":\"V\u00ec sao giai th\u1eeba t\u0103ng nhanh nh\u01b0 v\u1eady?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"V\u00ec m\u1ed7i b\u01b0\u1edbc ta nh\u00e2n th\u00eam m\u1ed9t s\u1ed1 l\u1edbn h\u01a1n, n\u00ean gi\u00e1 tr\u1ecb t\u0103ng theo c\u1ea5p s\u1ed1 nh\u00e2n d\u1ed3n; ch\u1ec9 \u0111\u1ebfn 10! \u0111\u00e3 h\u01a1n 3,6 tri\u1ec7u.\"}}]}\n<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Giai th\u1eeba c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean n, k\u00fd hi\u1ec7u n!, l\u00e0 t\u00edch c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 nguy\u00ean d\u01b0\u01a1ng t\u1eeb 1 \u0111\u1ebfn n: n! = 1 \u00d7 2 \u00d7 3 \u00d7 \u2026 \u00d7 n. \u0110\u1eb7c bi\u1ec7t, ng\u01b0\u1eddi ta quy \u01b0\u1edbc 0! = 1. \u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng kh\u00e1i ni\u1ec7m n\u1ec1n t\u1ea3ng c\u1ee7a to\u00e1n [&hellip;]<\/p>\n","protected":false},"author":102,"featured_media":571007,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"giai th\u1eeba l\u00e0 g\u00ec","_yoast_wpseo_title":"Giai th\u1eeba l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c n!, b\u1ea3ng gi\u00e1 tr\u1ecb v\u00e0 \u1ee9ng d\u1ee5ng","_yoast_wpseo_metadesc":"Giai th\u1eeba l\u00e0 g\u00ec? \u0110\u1ecbnh ngh\u0129a n!, quy \u01b0\u1edbc 0!=1, c\u00f4ng th\u1ee9c truy h\u1ed3i, b\u1ea3ng gi\u00e1 tr\u1ecb 0!-10! c\u00f9ng \u1ee9ng d\u1ee5ng ho\u00e1n v\u1ecb, t\u1ed5 h\u1ee3p v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i.","footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-570990","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Giai th\u1eeba l\u00e0 g\u00ec? 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