{"id":567429,"date":"2026-07-21T09:18:36","date_gmt":"2026-07-21T02:18:36","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567429"},"modified":"2026-07-21T15:29:36","modified_gmt":"2026-07-21T08:29:36","slug":"uoc-so-la-gi","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/uoc-so-la-gi\/","title":{"rendered":"\u01af\u1edbc s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch t\u00ecm \u01b0\u1edbc, \u01b0\u1edbc chung v\u00e0 \u01b0\u1edbc chung l\u1edbn nh\u1ea5t"},"content":{"rendered":"

\u01af\u1edbc s\u1ed1 (hay \u01b0\u1edbc) c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean a l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean m\u00e0 a chia h\u1ebft cho n\u00f3.<\/strong> N\u00f3i c\u00e1ch kh\u00e1c, n\u1ebfu a chia h\u1ebft cho b th\u00ec b \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u01b0\u1edbc c\u1ee7a a, \u0111\u1ed3ng th\u1eddi a l\u00e0 b\u1ed9i c\u1ee7a b. \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n c\u1ee7a To\u00e1n l\u1edbp 6, g\u1eafn li\u1ec1n v\u1edbi b\u1ed9i s\u1ed1, s\u1ed1 nguy\u00ean t\u1ed1, \u01b0\u1edbc chung v\u00e0 \u01b0\u1edbc chung l\u1edbn nh\u1ea5t, \u0111\u1ed3ng th\u1eddi c\u00f2n theo b\u1ea1n su\u1ed1t c\u00e1c b\u00e0i to\u00e1n v\u1ec1 ph\u00e2n s\u1ed1, chia h\u1ebft hay r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c \u1edf l\u1edbp tr\u00ean. N\u1ed9i dung d\u01b0\u1edbi \u0111\u00e2y tr\u00ecnh b\u00e0y kh\u00e1i ni\u1ec7m \u01b0\u1edbc s\u1ed1, c\u00e1ch t\u00ecm \u01b0\u1edbc nhanh, ba c\u00e1ch t\u00ecm \u01afCLN, c\u00e1ch ph\u00e2n bi\u1ec7t \u01b0\u1edbc v\u1edbi b\u1ed9i v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i t\u1eebng b\u01b0\u1edbc.<\/p>\n

Tr\u01b0\u1edbc khi luy\u1ec7n t\u00ecm \u01b0\u1edbc s\u1ed1, c\u00e1c em n\u00ean n\u1eafm ch\u1eafc b\u1ea3ng c\u1eedu ch\u01b0\u01a1ng<\/a> \u2014 c\u00f4ng c\u1ee5 gi\u00fap nh\u00e2n chia nhanh v\u00e0 x\u00e1c \u0111\u1ecbnh \u01b0\u1edbc, b\u1ed9i ch\u00ednh x\u00e1c h\u01a1n.<\/p>\n

\u01af\u1edbc s\u1ed1 l\u00e0 g\u00ec?<\/h2>\n

\u01af\u1edbc s\u1ed1 c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean a l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean m\u00e0 a chia h\u1ebft cho n\u00f3. N\u1ebfu s\u1ed1 t\u1ef1 nhi\u00ean a chia h\u1ebft cho s\u1ed1 t\u1ef1 nhi\u00ean b (b kh\u00e1c 0) th\u00ec ta n\u00f3i b l\u00e0 \u01b0\u1edbc c\u1ee7a a, c\u00f2n a l\u00e0 b\u1ed9i c\u1ee7a b. V\u00ed d\u1ee5, 12 chia h\u1ebft cho 3 n\u00ean 3 l\u00e0 \u01b0\u1edbc c\u1ee7a 12 v\u00e0 12 l\u00e0 b\u1ed9i c\u1ee7a 3. T\u1eadp h\u1ee3p c\u00e1c \u01b0\u1edbc c\u1ee7a a \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 \u01af(a). M\u1ed9t v\u00e0i t\u00ednh ch\u1ea5t c\u1ea7n nh\u1edb:<\/p>\n

    \n
  • S\u1ed1 1 l\u00e0 \u01b0\u1edbc c\u1ee7a m\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean, v\u00e0 m\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean kh\u00e1c 0 \u0111\u1ec1u l\u00e0 \u01b0\u1edbc c\u1ee7a ch\u00ednh n\u00f3.<\/li>\n
  • S\u1ed1 0 kh\u00f4ng bao gi\u1edd l\u00e0 \u01b0\u1edbc c\u1ee7a s\u1ed1 n\u00e0o (v\u00ec kh\u00f4ng th\u1ec3 chia cho 0), nh\u01b0ng 0 l\u00e0 b\u1ed9i c\u1ee7a m\u1ecdi s\u1ed1.<\/li>\n
  • M\u1ed7i s\u1ed1 t\u1ef1 nhi\u00ean kh\u00e1c 0 ch\u1ec9 c\u00f3 h\u1eefu h\u1ea1n \u01b0\u1edbc, \u01b0\u1edbc l\u1edbn nh\u1ea5t ch\u00ednh l\u00e0 b\u1ea3n th\u00e2n s\u1ed1 \u0111\u00f3.<\/li>\n<\/ul>\n

    \"uoc-so-la-gi-1\"<\/p>\n

    C\u00e1ch t\u00ecm \u01b0\u1edbc c\u1ee7a m\u1ed9t s\u1ed1<\/h2>\n

    C\u00e1ch c\u01a1 b\u1ea3n nh\u1ea5t l\u00e0 l\u1ea7n l\u01b0\u1ee3t chia s\u1ed1 a cho c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 1 \u0111\u1ebfn a, s\u1ed1 n\u00e0o chia h\u1ebft th\u00ec \u0111\u00f3 l\u00e0 \u01b0\u1edbc. Tuy nhi\u00ean c\u00e1ch n\u00e0y r\u1ea5t ch\u1eadm v\u1edbi s\u1ed1 l\u1edbn, n\u00ean tr\u00ean th\u1ef1c t\u1ebf b\u1ea1n ch\u1ec9 c\u1ea7n x\u00e9t c\u00e1c s\u1ed1 t\u1eeb 1 \u0111\u1ebfn c\u0103n b\u1eadc hai c\u1ee7a a r\u1ed3i gh\u00e9p c\u1eb7p: n\u1ebfu b l\u00e0 \u01b0\u1edbc th\u00ec a : b c\u0169ng l\u00e0 \u01b0\u1edbc.<\/p>\n

    V\u00ed d\u1ee5 v\u1edbi a = 36:<\/strong><\/p>\n

      \n
    • 36 : 1 = 36 \u2192 \u0111\u01b0\u1ee3c c\u1eb7p \u01b0\u1edbc (1; 36).<\/li>\n
    • 36 : 2 = 18 \u2192 \u0111\u01b0\u1ee3c c\u1eb7p (2; 18).<\/li>\n
    • 36 : 3 = 12 \u2192 \u0111\u01b0\u1ee3c c\u1eb7p (3; 12).<\/li>\n
    • 36 : 4 = 9 \u2192 \u0111\u01b0\u1ee3c c\u1eb7p (4; 9).<\/li>\n
    • 36 : 6 = 6 \u2192 \u0111\u01b0\u1ee3c \u01b0\u1edbc 6 (c\u1eb7p tr\u00f9ng nhau n\u00ean ch\u1ec9 t\u00ednh m\u1ed9t l\u1ea7n).<\/li>\n<\/ul>\n

      D\u1eebng l\u1ea1i \u1edf 6 v\u00ec 6 \u00d7 6 = 36. V\u1eady \u01af(36) = {1; 2; 3; 4; 6; 9; 12; 18; 36}, g\u1ed3m 9 \u01b0\u1edbc. C\u00e1ch gh\u00e9p c\u1eb7p n\u00e0y gi\u00fap b\u1ea1n li\u1ec7t k\u00ea \u01b0\u1edbc c\u1ee7a s\u1ed1 c\u00f3 ba ch\u1eef s\u1ed1 ch\u1ec9 trong v\u00e0i ch\u1ee5c gi\u00e2y.<\/p>\n

      B\u1ea3ng \u01b0\u1edbc c\u1ee7a m\u1ed9t s\u1ed1 s\u1ed1 th\u01b0\u1eddng g\u1eb7p<\/h2>\n

      B\u1ea3ng d\u01b0\u1edbi \u0111\u00e2y t\u1ed5ng h\u1ee3p t\u1eadp \u01b0\u1edbc c\u1ee7a nh\u1eefng s\u1ed1 hay xu\u1ea5t hi\u1ec7n trong b\u00e0i t\u1eadp l\u1edbp 6, k\u00e8m d\u1ea1ng ph\u00e2n t\u00edch ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 \u0111\u1ec3 b\u1ea1n \u0111\u1ed1i chi\u1ebfu.<\/p>\n\n\n\n\n\n\n\n\n\n\n
      S\u1ed1<\/th>\nPh\u00e2n t\u00edch ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1<\/th>\nT\u1eadp \u01b0\u1edbc<\/th>\nS\u1ed1 l\u01b0\u1ee3ng \u01b0\u1edbc<\/th>\n<\/tr>\n<\/thead>\n
      12<\/td>\n2\u00b2 \u00d7 3<\/td>\n1; 2; 3; 4; 6; 12<\/td>\n6<\/td>\n<\/tr>\n
      18<\/td>\n2 \u00d7 3\u00b2<\/td>\n1; 2; 3; 6; 9; 18<\/td>\n6<\/td>\n<\/tr>\n
      20<\/td>\n2\u00b2 \u00d7 5<\/td>\n1; 2; 4; 5; 10; 20<\/td>\n6<\/td>\n<\/tr>\n
      24<\/td>\n2\u00b3 \u00d7 3<\/td>\n1; 2; 3; 4; 6; 8; 12; 24<\/td>\n8<\/td>\n<\/tr>\n
      30<\/td>\n2 \u00d7 3 \u00d7 5<\/td>\n1; 2; 3; 5; 6; 10; 15; 30<\/td>\n8<\/td>\n<\/tr>\n
      36<\/td>\n2\u00b2 \u00d7 3\u00b2<\/td>\n1; 2; 3; 4; 6; 9; 12; 18; 36<\/td>\n9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

      \u0110\u1ebfm nhanh s\u1ed1 l\u01b0\u1ee3ng \u01b0\u1edbc b\u1eb1ng th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n

      Khi \u0111\u1ec1 b\u00e0i ch\u1ec9 h\u1ecfi “s\u1ed1 \u0111\u00f3 c\u00f3 bao nhi\u00eau \u01b0\u1edbc” m\u00e0 kh\u00f4ng c\u1ea7n li\u1ec7t k\u00ea, b\u1ea1n kh\u00f4ng ph\u1ea3i vi\u1ebft ra t\u1eebng \u01b0\u1edbc. N\u1ebfu ph\u00e2n t\u00edch \u0111\u01b0\u1ee3c a = p\u2081^m \u00d7 p\u2082^n \u00d7 \u2026 th\u00ec s\u1ed1 l\u01b0\u1ee3ng \u01b0\u1edbc c\u1ee7a a b\u1eb1ng t\u00edch (m + 1)(n + 1)\u2026<\/p>\n

        \n
      • V\u1edbi 36 = 2\u00b2 \u00d7 3\u00b2:<\/strong> s\u1ed1 \u01b0\u1edbc l\u00e0 (2 + 1)(2 + 1) = 9 \u01b0\u1edbc, \u0111\u00fang b\u1eb1ng k\u1ebft qu\u1ea3 li\u1ec7t k\u00ea \u1edf tr\u00ean.<\/li>\n
      • V\u1edbi 60 = 2\u00b2 \u00d7 3 \u00d7 5:<\/strong> s\u1ed1 \u01b0\u1edbc l\u00e0 (2 + 1)(1 + 1)(1 + 1) = 12 \u01b0\u1edbc, g\u1ed3m 1; 2; 3; 4; 5; 6; 10; 12; 15; 20; 30; 60.<\/li>\n
      • V\u1edbi 100 = 2\u00b2 \u00d7 5\u00b2:<\/strong> s\u1ed1 \u01b0\u1edbc l\u00e0 (2 + 1)(2 + 1) = 9 \u01b0\u1edbc, g\u1ed3m 1; 2; 4; 5; 10; 20; 25; 50; 100.<\/li>\n<\/ul>\n

        \"uoc-so-la-gi-2\"<\/p>\n

        \u01af\u1edbc chung v\u00e0 \u01b0\u1edbc chung l\u1edbn nh\u1ea5t<\/h2>\n

        \u01af\u1edbc chung c\u1ee7a hai hay nhi\u1ec1u s\u1ed1 l\u00e0 \u01b0\u1edbc c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 \u0111\u00f3, c\u00f2n \u01b0\u1edbc chung l\u1edbn nh\u1ea5t (\u01afCLN) l\u00e0 s\u1ed1 l\u1edbn nh\u1ea5t trong c\u00e1c \u01b0\u1edbc chung. C\u00f3 ba c\u00e1ch t\u00ecm \u01afCLN, b\u1ea1n ch\u1ecdn c\u00e1ch ph\u00f9 h\u1ee3p v\u1edbi \u0111\u1ed9 l\u1edbn c\u1ee7a s\u1ed1.<\/p>\n

        C\u00e1ch 1: Li\u1ec7t k\u00ea \u01b0\u1edbc r\u1ed3i so s\u00e1nh<\/h3>\n

        Ph\u00f9 h\u1ee3p v\u1edbi s\u1ed1 nh\u1ecf. V\u00ed d\u1ee5 t\u00ecm \u01afCLN(12, 18):<\/p>\n

          \n
        • \u01af(12) = {1; 2; 3; 4; 6; 12}; \u01af(18) = {1; 2; 3; 6; 9; 18}.<\/li>\n
        • \u01af\u1edbc chung c\u1ee7a 12 v\u00e0 18 l\u00e0 {1; 2; 3; 6}.<\/li>\n
        • S\u1ed1 l\u1edbn nh\u1ea5t trong t\u1eadp \u0111\u00f3 l\u00e0 6, v\u1eady \u01afCLN(12, 18) = 6.<\/li>\n<\/ul>\n

          C\u00e1ch 2: Ph\u00e2n t\u00edch ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1<\/h3>\n

          Ph\u00e2n t\u00edch m\u1ed7i s\u1ed1 ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1, r\u1ed3i l\u1ea5y t\u00edch c\u00e1c th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 chung<\/em> v\u1edbi s\u1ed1 m\u0169 nh\u1ecf nh\u1ea5t<\/em>. V\u00ed d\u1ee5 t\u00ecm \u01afCLN(24, 36):<\/p>\n

            \n
          • 24 = 2\u00b3 \u00d7 3; 36 = 2\u00b2 \u00d7 3\u00b2.<\/li>\n
          • Th\u1eeba s\u1ed1 chung l\u00e0 2 v\u00e0 3; s\u1ed1 m\u0169 nh\u1ecf nh\u1ea5t l\u1ea7n l\u01b0\u1ee3t l\u00e0 2 v\u00e0 1.<\/li>\n
          • V\u1eady \u01afCLN(24, 36) = 2\u00b2 \u00d7 3 = 12.<\/li>\n<\/ul>\n

            C\u00e1ch 3: Thu\u1eadt to\u00e1n Euclid (chia li\u00ean ti\u1ebfp)<\/h3>\n

            V\u1edbi s\u1ed1 l\u1edbn, c\u00e1ch nhanh nh\u1ea5t l\u00e0 l\u1ea5y s\u1ed1 l\u1edbn chia s\u1ed1 b\u00e9, r\u1ed3i thay s\u1ed1 l\u1edbn b\u1eb1ng s\u1ed1 b\u00e9 v\u00e0 s\u1ed1 b\u00e9 b\u1eb1ng s\u1ed1 d\u01b0, l\u1eb7p \u0111\u1ebfn khi d\u01b0 b\u1eb1ng 0. V\u00ed d\u1ee5 t\u00ecm \u01afCLN(72, 60):<\/p>\n

              \n
            • 72 : 60 \u0111\u01b0\u1ee3c 1, d\u01b0 12.<\/li>\n
            • 60 : 12 \u0111\u01b0\u1ee3c 5, d\u01b0 0 \u2192 d\u1eebng l\u1ea1i.<\/li>\n
            • S\u1ed1 chia cu\u1ed1i c\u00f9ng kh\u00e1c 0 l\u00e0 12, v\u1eady \u01afCLN(72, 60) = 12.<\/li>\n<\/ul>\n

              Hai s\u1ed1 c\u00f3 \u01afCLN b\u1eb1ng 1 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 hai s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau, ch\u1eb3ng h\u1ea1n 8 v\u00e0 15 v\u00ec \u01af(8) = {1; 2; 4; 8} v\u00e0 \u01af(15) = {1; 3; 5; 15} ch\u1ec9 c\u00f3 duy nh\u1ea5t \u01b0\u1edbc chung l\u00e0 1.<\/p>\n

              \u01af\u1edbc s\u1ed1 v\u00e0 s\u1ed1 nguy\u00ean t\u1ed1<\/h2>\n

              S\u1ed1 l\u01b0\u1ee3ng \u01b0\u1edbc ch\u00ednh l\u00e0 c\u0103n c\u1ee9 \u0111\u1ec3 ph\u00e2n lo\u1ea1i s\u1ed1 t\u1ef1 nhi\u00ean. M\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n 1 ch\u1ec9 c\u00f3 \u0111\u00fang hai \u01b0\u1edbc l\u00e0 1 v\u00e0 ch\u00ednh n\u00f3 th\u00ec \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1<\/strong>, v\u00ed d\u1ee5 2, 3, 5, 7, 11, 13. Ng\u01b0\u1ee3c l\u1ea1i, s\u1ed1 t\u1ef1 nhi\u00ean l\u1edbn h\u01a1n 1 c\u00f3 nhi\u1ec1u h\u01a1n hai \u01b0\u1edbc g\u1ecdi l\u00e0 h\u1ee3p s\u1ed1, v\u00ed d\u1ee5 4, 6, 8, 9. S\u1ed1 1 ch\u1ec9 c\u00f3 m\u1ed9t \u01b0\u1edbc l\u00e0 ch\u00ednh n\u00f3 n\u00ean kh\u00f4ng ph\u1ea3i s\u1ed1 nguy\u00ean t\u1ed1 c\u0169ng kh\u00f4ng ph\u1ea3i h\u1ee3p s\u1ed1; s\u1ed1 0 th\u00ec c\u00f3 v\u00f4 s\u1ed1 \u01b0\u1edbc n\u00ean c\u0169ng kh\u00f4ng x\u1ebfp v\u00e0o hai nh\u00f3m n\u00e0y. Ri\u00eang s\u1ed1 2 l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1 ch\u1eb5n duy nh\u1ea5t, m\u1ecdi s\u1ed1 ch\u1eb5n l\u1edbn h\u01a1n 2 \u0111\u1ec1u c\u00f3 th\u00eam \u01b0\u1edbc 2 n\u00ean ch\u1eafc ch\u1eafn l\u00e0 h\u1ee3p s\u1ed1.<\/p>\n

              \"uoc-so-la-gi-3\"<\/p>\n

              Ph\u00e2n bi\u1ec7t \u01b0\u1edbc s\u1ed1 v\u00e0 b\u1ed9i s\u1ed1<\/h2>\n

              \u01af\u1edbc v\u00e0 b\u1ed9i l\u00e0 hai kh\u00e1i ni\u1ec7m ng\u01b0\u1ee3c chi\u1ec1u nhau nh\u01b0ng lu\u00f4n xu\u1ea5t hi\u1ec7n c\u00f9ng l\u00fac, b\u1ea3ng sau gi\u00fap b\u1ea1n kh\u00f4ng nh\u1ea7m khi \u0111\u1ecdc \u0111\u1ec1.<\/p>\n\n\n\n\n\n\n\n\n\n
              Ti\u00eau ch\u00ed<\/th>\n\u01af\u1edbc s\u1ed1<\/th>\nB\u1ed9i s\u1ed1<\/th>\n<\/tr>\n<\/thead>\n
              \u0110\u1ecbnh ngh\u0129a<\/td>\nb l\u00e0 \u01b0\u1edbc c\u1ee7a a khi a chia h\u1ebft cho b<\/td>\na l\u00e0 b\u1ed9i c\u1ee7a b khi a chia h\u1ebft cho b<\/td>\n<\/tr>\n
              C\u00e1ch t\u00ecm<\/td>\nChia a cho c\u00e1c s\u1ed1 t\u1eeb 1 \u0111\u1ebfn a<\/td>\nNh\u00e2n b l\u1ea7n l\u01b0\u1ee3t v\u1edbi 0; 1; 2; 3\u2026<\/td>\n<\/tr>\n
              S\u1ed1 l\u01b0\u1ee3ng<\/td>\nH\u1eefu h\u1ea1n<\/td>\nV\u00f4 s\u1ed1<\/td>\n<\/tr>\n
              \u0110\u1ed9 l\u1edbn<\/td>\nKh\u00f4ng v\u01b0\u1ee3t qu\u00e1 a<\/td>\nKh\u00f4ng nh\u1ecf h\u01a1n b (tr\u1eeb b\u1ed9i 0)<\/td>\n<\/tr>\n
              V\u00ed d\u1ee5 v\u1edbi 12 v\u00e0 3<\/td>\n3 l\u00e0 \u01b0\u1edbc c\u1ee7a 12<\/td>\n12 l\u00e0 b\u1ed9i c\u1ee7a 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

              \u0110i k\u00e8m v\u1edbi \u01afCLN l\u00e0 b\u1ed9i chung nh\u1ecf nh\u1ea5t (BCNN). Hai \u0111\u1ea1i l\u01b0\u1ee3ng n\u00e0y li\u00ean h\u1ec7 v\u1edbi nhau qua c\u00f4ng th\u1ee9c \u01afCLN(a, b) \u00d7 BCNN(a, b) = a \u00d7 b, r\u1ea5t ti\u1ec7n \u0111\u1ec3 ki\u1ec3m tra l\u1ea1i k\u1ebft qu\u1ea3: v\u1edbi a = 12, b = 18 th\u00ec 6 \u00d7 36 = 216 = 12 \u00d7 18.<\/p>\n

              \u1ee8ng d\u1ee5ng c\u1ee7a \u01b0\u1edbc s\u1ed1 trong b\u00e0i to\u00e1n th\u1ef1c t\u1ebf<\/h2>\n

              \u01af\u1edbc s\u1ed1 kh\u00f4ng ch\u1ec9 n\u1eb1m trong s\u00e1ch gi\u00e1o khoa m\u00e0 xu\u1ea5t hi\u1ec7n \u1edf nhi\u1ec1u b\u00e0i to\u00e1n chia ph\u1ea7n b\u1eb1ng nhau.<\/p>\n

                \n
              • Chia qu\u00e0 \u0111\u1ec1u nhau:<\/strong> c\u00f3 24 chi\u1ebfc b\u00fat v\u00e0 36 quy\u1ec3n v\u1edf, mu\u1ed1n chia th\u00e0nh nhi\u1ec1u ph\u1ea7n b\u1eb1ng nhau nh\u1ea5t th\u00ec s\u1ed1 ph\u1ea7n ch\u00ednh l\u00e0 \u01afCLN(24, 36) = 12, m\u1ed7i ph\u1ea7n g\u1ed3m 2 b\u00fat v\u00e0 3 v\u1edf.<\/li>\n
              • R\u00fat g\u1ecdn ph\u00e2n s\u1ed1:<\/strong> mu\u1ed1n r\u00fat g\u1ecdn 18\/24 v\u1ec1 t\u1ed1i gi\u1ea3n, ta chia c\u1ea3 t\u1eed v\u00e0 m\u1eabu cho \u01afCLN(18, 24) = 6 v\u00e0 \u0111\u01b0\u1ee3c 3\/4.<\/li>\n
              • C\u1eaft v\u1eadt li\u1ec7u:<\/strong> c\u1eaft hai thanh g\u1ed7 d\u00e0i 60 cm v\u00e0 72 cm th\u00e0nh c\u00e1c \u0111o\u1ea1n b\u1eb1ng nhau, d\u00e0i nh\u1ea5t c\u00f3 th\u1ec3 m\u00e0 kh\u00f4ng th\u1eeba, th\u00ec m\u1ed7i \u0111o\u1ea1n d\u00e0i \u01afCLN(60, 72) = 12 cm.<\/li>\n<\/ul>\n

                B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n
                  \n
                • B\u00e0i 1:<\/strong> T\u00ecm t\u1ea5t c\u1ea3 c\u00e1c \u01b0\u1edbc c\u1ee7a 20. L\u1eddi gi\u1ea3i:<\/em> L\u1ea7n l\u01b0\u1ee3t chia 20 cho 1; 2; 4 (d\u1eebng \u1edf 4 v\u00ec 4 \u00d7 5 = 20) ta \u0111\u01b0\u1ee3c c\u00e1c c\u1eb7p (1; 20), (2; 10), (4; 5). V\u1eady \u01af(20) = {1; 2; 4; 5; 10; 20}.<\/li>\n
                • B\u00e0i 2:<\/strong> S\u1ed1 7 c\u00f3 ph\u1ea3i s\u1ed1 nguy\u00ean t\u1ed1 kh\u00f4ng? L\u1eddi gi\u1ea3i:<\/em> 7 kh\u00f4ng chia h\u1ebft cho 2, 3 v\u00e0 2 \u00d7 2 = 4 < 7 < 3 \u00d7 3 = 9 n\u00ean ch\u1ec9 c\u1ea7n x\u00e9t \u0111\u1ebfn 2. V\u00ec 7 ch\u1ec9 c\u00f3 hai \u01b0\u1edbc l\u00e0 1 v\u00e0 7 n\u00ean 7 l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1.<\/li>\n
                • B\u00e0i 3:<\/strong> T\u00ecm \u01b0\u1edbc chung l\u1edbn nh\u1ea5t c\u1ee7a 8 v\u00e0 12. L\u1eddi gi\u1ea3i:<\/em> \u01af(8) = {1; 2; 4; 8}, \u01af(12) = {1; 2; 3; 4; 6; 12}, \u01b0\u1edbc chung l\u00e0 {1; 2; 4} n\u00ean \u01afCLN(8, 12) = 4.<\/li>\n
                • B\u00e0i 4:<\/strong> S\u1ed1 9 l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1 hay h\u1ee3p s\u1ed1? L\u1eddi gi\u1ea3i:<\/em> 9 chia h\u1ebft cho 1, 3 v\u00e0 9 n\u00ean \u01af(9) = {1; 3; 9}. C\u00f3 ba \u01b0\u1edbc, nhi\u1ec1u h\u01a1n hai, v\u1eady 9 l\u00e0 h\u1ee3p s\u1ed1.<\/li>\n
                • B\u00e0i 5:<\/strong> S\u1ed1 48 c\u00f3 bao nhi\u00eau \u01b0\u1edbc? L\u1eddi gi\u1ea3i:<\/em> 48 = 2\u2074 \u00d7 3, s\u1ed1 \u01b0\u1edbc l\u00e0 (4 + 1)(1 + 1) = 10 \u01b0\u1edbc, \u0111\u00f3 l\u00e0 1; 2; 3; 4; 6; 8; 12; 16; 24; 48.<\/li>\n
                • B\u00e0i 6:<\/strong> D\u00f9ng thu\u1eadt to\u00e1n Euclid t\u00ecm \u01afCLN(48, 18). L\u1eddi gi\u1ea3i:<\/em> 48 : 18 \u0111\u01b0\u1ee3c 2 d\u01b0 12; 18 : 12 \u0111\u01b0\u1ee3c 1 d\u01b0 6; 12 : 6 \u0111\u01b0\u1ee3c 2 d\u01b0 0. S\u1ed1 chia cu\u1ed1i kh\u00e1c 0 l\u00e0 6, v\u1eady \u01afCLN(48, 18) = 6.<\/li>\n
                • B\u00e0i 7 (tr\u1eafc nghi\u1ec7m):<\/strong> S\u1ed1 n\u00e0o sau \u0111\u00e2y l\u00e0 \u01b0\u1edbc c\u1ee7a 15? A. 4 \u2014 B. 5 \u2014 C. 7 \u2014 D. 8. \u0110\u00e1p \u00e1n:<\/em> B, v\u00ec 15 : 5 = 3 chia h\u1ebft, c\u00f2n 15 chia cho 4, 7, 8 \u0111\u1ec1u c\u00f3 d\u01b0.<\/li>\n<\/ul>\n

                  \"uoc-so-la-gi-4\"<\/p>\n

                  C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 \u01b0\u1edbc s\u1ed1<\/h2>\n

                  \u01af\u1edbc s\u1ed1 l\u00e0 g\u00ec?<\/h3>\n

                  L\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean m\u00e0 m\u1ed9t s\u1ed1 kh\u00e1c chia h\u1ebft cho n\u00f3; n\u1ebfu a chia h\u1ebft cho b th\u00ec b l\u00e0 \u01b0\u1edbc c\u1ee7a a.<\/p>\n

                  C\u00e1ch t\u00ecm \u01b0\u1edbc c\u1ee7a m\u1ed9t s\u1ed1?<\/h3>\n

                  L\u1ea7n l\u01b0\u1ee3t chia s\u1ed1 \u0111\u00f3 cho c\u00e1c s\u1ed1 t\u1eeb 1 \u0111\u1ebfn c\u0103n b\u1eadc hai c\u1ee7a n\u00f3 r\u1ed3i gh\u00e9p c\u1eb7p, s\u1ed1 n\u00e0o chia h\u1ebft th\u00ec c\u1ea3 n\u00f3 v\u00e0 th\u01b0\u01a1ng \u0111\u1ec1u l\u00e0 \u01b0\u1edbc.<\/p>\n

                  \u01af\u1edbc chung l\u1edbn nh\u1ea5t l\u00e0 g\u00ec?<\/h3>\n

                  L\u00e0 s\u1ed1 l\u1edbn nh\u1ea5t trong c\u00e1c \u01b0\u1edbc chung c\u1ee7a hai hay nhi\u1ec1u s\u1ed1, v\u00ed d\u1ee5 \u01afCLN(12, 18) = 6.<\/p>\n

                  \u01af(12) g\u1ed3m nh\u1eefng s\u1ed1 n\u00e0o?<\/h3>\n

                  \u01af(12) = {1; 2; 3; 4; 6; 12}, t\u1ed5ng c\u1ed9ng 6 \u01b0\u1edbc.<\/p>\n

                  S\u1ed1 nguy\u00ean t\u1ed1 c\u00f3 m\u1ea5y \u01b0\u1edbc?<\/h3>\n

                  S\u1ed1 nguy\u00ean t\u1ed1 ch\u1ec9 c\u00f3 \u0111\u00fang hai \u01b0\u1edbc l\u00e0 1 v\u00e0 ch\u00ednh n\u00f3.<\/p>\n

                  S\u1ed1 1 c\u00f3 ph\u1ea3i l\u00e0 \u01b0\u1edbc c\u1ee7a m\u1ecdi s\u1ed1 kh\u00f4ng?<\/h3>\n

                  \u0110\u00fang, s\u1ed1 1 l\u00e0 \u01b0\u1edbc c\u1ee7a m\u1ecdi s\u1ed1 t\u1ef1 nhi\u00ean, c\u00f2n s\u1ed1 0 kh\u00f4ng ph\u1ea3i l\u00e0 \u01b0\u1edbc c\u1ee7a b\u1ea5t k\u1ef3 s\u1ed1 n\u00e0o.<\/p>\n

                  L\u00e0m sao bi\u1ebft m\u1ed9t s\u1ed1 c\u00f3 bao nhi\u00eau \u01b0\u1edbc m\u00e0 kh\u00f4ng c\u1ea7n li\u1ec7t k\u00ea?<\/h3>\n

                  Ph\u00e2n t\u00edch s\u1ed1 \u0111\u00f3 ra th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 d\u1ea1ng p\u2081^m \u00d7 p\u2082^n, r\u1ed3i nh\u00e2n c\u00e1c s\u1ed1 m\u0169 \u0111\u00e3 c\u1ed9ng th\u00eam 1: s\u1ed1 \u01b0\u1edbc b\u1eb1ng (m + 1)(n + 1).<\/p>\n