{"id":567246,"date":"2026-07-22T09:23:17","date_gmt":"2026-07-22T02:23:17","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=567246"},"modified":"2026-07-22T09:23:17","modified_gmt":"2026-07-22T02:23:17","slug":"boi-so","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/boi-so\/","title":{"rendered":"B\u1ed9i s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch t\u00ecm b\u1ed9i, b\u1ed9i chung v\u00e0 BCNN"},"content":{"rendered":"

B\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean a (kh\u00e1c 0) l\u00e0 nh\u1eefng s\u1ed1 chia h\u1ebft cho a; t\u1eadp h\u1ee3p c\u00e1c b\u1ed9i c\u1ee7a a g\u1ed3m 0, a, 2a, 3a, 4a\u2026 N\u00f3i c\u00e1ch kh\u00e1c, n\u1ebfu s\u1ed1 t\u1ef1 nhi\u00ean b chia h\u1ebft cho a th\u00ec b l\u00e0 b\u1ed9i c\u1ee7a a. B\u1ed9i s\u1ed1 l\u00e0 ki\u1ebfn th\u1ee9c n\u1ec1n t\u1ea3ng c\u1ee7a To\u00e1n l\u1edbp 6, g\u1eafn li\u1ec1n v\u1edbi \u01b0\u1edbc s\u1ed1, b\u1ed9i chung v\u00e0 b\u1ed9i chung nh\u1ecf nh\u1ea5t. B\u00e0i vi\u1ebft n\u00e0y tr\u00ecnh b\u00e0y <\/span>b\u1ed9i s\u1ed1 l\u00e0 g\u00ec<\/b>, c\u00e1ch t\u00ecm b\u1ed9i, b\u1ed9i chung \u2013 BCNN, quan h\u1ec7 \u01b0\u1edbc \u2013 b\u1ed9i v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i.<\/span><\/p>\n

B\u1ed9i s\u1ed1 l\u00e0 g\u00ec?<\/b><\/h2>\n

B\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean a l\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean chia h\u1ebft cho a. N\u1ebfu b chia h\u1ebft cho a th\u00ec b l\u00e0 b\u1ed9i c\u1ee7a a, \u0111\u1ed3ng th\u1eddi a l\u00e0 \u01b0\u1edbc c\u1ee7a b. V\u00ed d\u1ee5, 12 chia h\u1ebft cho 3, n\u00ean 12 l\u00e0 b\u1ed9i c\u1ee7a 3 v\u00e0 3 l\u00e0 \u01b0\u1edbc c\u1ee7a 12. B\u1ed9i v\u00e0 \u01b0\u1edbc l\u00e0 hai kh\u00e1i ni\u1ec7m lu\u00f4n \u0111i c\u00f9ng nhau.<\/span><\/p>\n

\"boi-so-1\"<\/p>\n

C\u00e1ch t\u00ecm b\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1<\/b><\/h2>\n

B\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 l\u00e0 c\u00e1c s\u1ed1 nh\u1eadn \u0111\u01b0\u1ee3c khi nh\u00e2n s\u1ed1 \u0111\u00f3 v\u1edbi m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean. \u0110\u1ec3 t\u00ecm c\u00e1c b\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean a (v\u1edbi a kh\u00e1c 0), ta l\u1ea7n l\u01b0\u1ee3t l\u1ea5y a nh\u00e2n v\u1edbi c\u00e1c s\u1ed1 0, 1, 2, 3, 4,… C\u00e1c k\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c ch\u00ednh l\u00e0 c\u00e1c b\u1ed9i c\u1ee7a a.<\/span><\/p>\n

T\u1eadp h\u1ee3p c\u00e1c b\u1ed9i c\u1ee7a s\u1ed1 a \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 B(a).<\/strong><\/span><\/p>\n

V\u00ed d\u1ee5:<\/span><\/p>\n

    \n
  • B(4) = {0; 4; 8; 12; 16; 20; …}<\/span><\/li>\n
  • V\u00ec c\u00f3 th\u1ec3 nh\u00e2n s\u1ed1 a v\u1edbi v\u00f4 s\u1ed1 s\u1ed1 t\u1ef1 nhi\u00ean kh\u00e1c nhau n\u00ean m\u1ed7i s\u1ed1 t\u1ef1 nhi\u00ean kh\u00e1c 0 c\u00f3 v\u00f4 s\u1ed1 b\u1ed9i.<\/span><\/li>\n<\/ul>\n

    B\u1ed9i chung v\u00e0 b\u1ed9i chung nh\u1ecf nh\u1ea5t<\/b><\/h2>\n

    B\u1ed9i s\u1ed1 l\u00e0 g\u00ec?<\/b> B\u1ed9i chung c\u1ee7a hai hay nhi\u1ec1u s\u1ed1 l\u00e0 nh\u1eefng s\u1ed1 \u0111\u1ed3ng th\u1eddi l\u00e0 b\u1ed9i c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c s\u1ed1 \u0111\u00f3. Trong c\u00e1c b\u1ed9i chung, s\u1ed1 nh\u1ecf nh\u1ea5t kh\u00e1c 0 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 b\u1ed9i chung nh\u1ecf nh\u1ea5t (BCNN) c\u1ee7a c\u00e1c s\u1ed1 \u0111\u00e3 cho.<\/span><\/p>\n

    \u0110\u1ec3 t\u00ecm b\u1ed9i chung v\u00e0 BCNN, ta c\u00f3 th\u1ec3 li\u1ec7t k\u00ea c\u00e1c b\u1ed9i c\u1ee7a t\u1eebng s\u1ed1, sau \u0111\u00f3 t\u00ecm nh\u1eefng s\u1ed1 xu\u1ea5t hi\u1ec7n trong t\u1ea5t c\u1ea3 c\u00e1c t\u1eadp h\u1ee3p b\u1ed9i.<\/span><\/p>\n

    V\u00ed d\u1ee5:<\/span><\/p>\n

      \n
    • B(4) = {0; 4; 8; 12; 16; 20; 24; …}<\/span><\/li>\n
    • B(6) = {0; 6; 12; 18; 24; …}<\/span><\/li>\n<\/ul>\n

      C\u00e1c s\u1ed1 xu\u1ea5t hi\u1ec7n trong c\u1ea3 hai t\u1eadp h\u1ee3p tr\u00ean l\u00e0 c\u00e1c b\u1ed9i chung c\u1ee7a 4 v\u00e0 6:<\/span><\/p>\n

        \n
      • B\u1ed9i chung c\u1ee7a 4 v\u00e0 6 l\u00e0 {0; 12; 24; …}<\/span><\/li>\n
      • Trong c\u00e1c b\u1ed9i chung kh\u00e1c 0, s\u1ed1 nh\u1ecf nh\u1ea5t l\u00e0 12. V\u00ec v\u1eady: BCNN(4, 6) = 12<\/span><\/li>\n<\/ul>\n

        \"boi-so-2\"<\/p>\n

        Quan h\u1ec7 gi\u1eefa \u01b0\u1edbc v\u00e0 b\u1ed9i<\/b><\/h2>\n

        \u01af\u1edbc v\u00e0 b\u1ed9i l\u00e0 hai kh\u00e1i ni\u1ec7m c\u00f3 m\u1ed1i quan h\u1ec7 ng\u01b0\u1ee3c nhau trong ph\u00e9p chia. N\u1ebfu s\u1ed1 a chia h\u1ebft cho s\u1ed1 b th\u00ec b l\u00e0 \u01b0\u1edbc c\u1ee7a a, \u0111\u1ed3ng th\u1eddi a l\u00e0 b\u1ed9i c\u1ee7a b.<\/span><\/p>\n

        V\u00ed d\u1ee5: V\u00ec 6 chia h\u1ebft cho 2 n\u00ean 2 l\u00e0 \u01b0\u1edbc c\u1ee7a 6, c\u00f2n 6 l\u00e0 b\u1ed9i c\u1ee7a 2.<\/span><\/p>\n

        M\u1ed9t \u0111i\u1ec3m c\u1ea7n l\u01b0u \u00fd l\u00e0 m\u1ed7i s\u1ed1 t\u1ef1 nhi\u00ean kh\u00e1c 0 c\u00f3 m\u1ed9t s\u1ed1 l\u01b0\u1ee3ng \u01b0\u1edbc h\u1eefu h\u1ea1n, t\u1ee9c l\u00e0 c\u00f3 th\u1ec3 li\u1ec7t k\u00ea \u0111\u1ea7y \u0111\u1ee7 c\u00e1c \u01b0\u1edbc c\u1ee7a n\u00f3. Ng\u01b0\u1ee3c l\u1ea1i, m\u1ed7i s\u1ed1 t\u1ef1 nhi\u00ean kh\u00e1c 0 l\u1ea1i c\u00f3 v\u00f4 s\u1ed1 b\u1ed9i v\u00ec c\u00f3 th\u1ec3 nh\u00e2n s\u1ed1 \u0111\u00f3 v\u1edbi v\u00f4 s\u1ed1 s\u1ed1 t\u1ef1 nhi\u00ean kh\u00e1c nhau.<\/span><\/p>\n

        V\u00ed d\u1ee5:<\/span><\/p>\n

          \n
        • S\u1ed1 6 c\u00f3 c\u00e1c \u01b0\u1edbc l\u00e0: 1, 2, 3, 6.<\/span><\/li>\n
        • S\u1ed1 6 c\u00f3 c\u00e1c b\u1ed9i l\u00e0: 0, 6, 12, 18, 24, …<\/span><\/li>\n<\/ul>\n

          V\u00ed d\u1ee5 v\u1ec1 b\u1ed9i s\u1ed1 l\u00e0 g\u00ec<\/b><\/h2>\n

          V\u00ed d\u1ee5 1: C\u00e1c b\u1ed9i c\u1ee7a 5 nh\u1ecf h\u01a1n 30 l\u00e0: 0, 5, 10, 15, 20, 25.<\/span><\/p>\n

          V\u00ed d\u1ee5 2: S\u1ed1 24 c\u00f3 ph\u1ea3i l\u00e0 b\u1ed9i c\u1ee7a 8 kh\u00f4ng? V\u00ec 24 chia h\u1ebft cho 8 (24 = 8 \u00d7 3) n\u00ean 24 l\u00e0 b\u1ed9i c\u1ee7a 8.<\/span><\/p>\n

          \"boi-so-3\"<\/p>\n

          B\u00e0i t\u1eadp v\u1eadn d\u1ee5ng c\u00f3 l\u1eddi gi\u1ea3i<\/strong><\/h2>\n

          B\u00e0i 1: T\u00ecm c\u00e1c b\u1ed9i c\u1ee7a 7 nh\u1ecf h\u01a1n 40. L\u1eddi gi\u1ea3i: 0, 7, 14, 21, 28, 35.<\/span><\/p>\n

          B\u00e0i 2: S\u1ed1 45 c\u00f3 l\u00e0 b\u1ed9i c\u1ee7a 9 kh\u00f4ng? L\u1eddi gi\u1ea3i: 45 chia h\u1ebft cho 9 (45 = 9 \u00d7 5) n\u00ean 45 l\u00e0 b\u1ed9i c\u1ee7a 9.<\/span><\/p>\n

          B\u00e0i 3: T\u00ecm b\u1ed9i chung nh\u1ecf nh\u1ea5t c\u1ee7a 6 v\u00e0 8. L\u1eddi gi\u1ea3i: B(6) = {0;6;12;18;24;\u2026}, B(8) = {0;8;16;24;\u2026}; b\u1ed9i chung nh\u1ecf nh\u1ea5t kh\u00e1c 0 l\u00e0 24, n\u00ean BCNN(6, 8) = 24.<\/span><\/p>\n

          B\u00e0i 4: Vi\u1ebft ba b\u1ed9i \u0111\u1ea7u ti\u00ean kh\u00e1c 0 c\u1ee7a 12. L\u1eddi gi\u1ea3i: 12, 24, 36.<\/span><\/p>\n

          B\u00e0i 5 (tr\u1eafc nghi\u1ec7m): S\u1ed1 n\u00e0o sau \u0111\u00e2y l\u00e0 b\u1ed9i c\u1ee7a 6? A. 15 B. 20 C. 24 D. 34. \u0110\u00e1p \u00e1n: C, v\u00ec 24 = 6 \u00d7 4.<\/span><\/p>\n

          \u1ee8ng d\u1ee5ng c\u1ee7a b\u1ed9i s\u1ed1 l\u00e0 g\u00ec<\/b><\/h2>\n

          B\u1ed9i s\u1ed1 v\u00e0 b\u1ed9i chung nh\u1ecf nh\u1ea5t (BCNN) c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng quan tr\u1ecdng trong to\u00e1n h\u1ecdc c\u0169ng nh\u01b0 trong th\u1ef1c t\u1ebf. Vi\u1ec7c hi\u1ec3u r\u00f5 c\u00e1c kh\u00e1i ni\u1ec7m n\u00e0y gi\u00fap ch\u00fang ta gi\u1ea3i quy\u1ebft nhanh ch\u00f3ng nhi\u1ec1u b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn s\u1ed1 h\u1ecdc v\u00e0 c\u00e1c t\u00ecnh hu\u1ed1ng c\u1ea7n t\u00ecm s\u1ef1 l\u1eb7p l\u1ea1i ho\u1eb7c s\u1eafp x\u1ebfp h\u1ee3p l\u00fd.<\/span><\/p>\n

          M\u1ed9t s\u1ed1 \u1ee9ng d\u1ee5ng ph\u1ed5 bi\u1ebfn c\u1ee7a b\u1ed9i s\u1ed1 v\u00e0 BCNN g\u1ed3m:<\/span><\/p>\n

            \n
          • Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 c\u00e1c ph\u00e2n s\u1ed1: BCNN c\u1ee7a c\u00e1c m\u1eabu s\u1ed1 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ecm m\u1eabu s\u1ed1 chung, gi\u00fap th\u1ef1c hi\u1ec7n ph\u00e9p c\u1ed9ng, tr\u1eeb c\u00e1c ph\u00e2n s\u1ed1 d\u1ec5 d\u00e0ng h\u01a1n.<\/span><\/li>\n
          • Gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n v\u1ec1 chu k\u1ef3 l\u1eb7p l\u1ea1i: Khi c\u00e1c s\u1ef1 ki\u1ec7n x\u1ea3y ra theo nh\u1eefng kho\u1ea3ng th\u1eddi gian kh\u00e1c nhau, BCNN gi\u00fap x\u00e1c \u0111\u1ecbnh th\u1eddi \u0111i\u1ec3m ch\u00fang c\u00f9ng l\u1eb7p l\u1ea1i. V\u00ed d\u1ee5 nh\u01b0 hai chuy\u1ebfn xe c\u00f9ng xu\u1ea5t ph\u00e1t v\u00e0 t\u00ecm th\u1eddi \u0111i\u1ec3m g\u1eb7p l\u1ea1i nhau.<\/span><\/li>\n
          • Chia nh\u00f3m v\u00e0 s\u1eafp x\u1ebfp \u0111\u1ec1u nhau: B\u1ed9i s\u1ed1 gi\u00fap x\u00e1c \u0111\u1ecbnh s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed ph\u00f9 h\u1ee3p \u0111\u1ec3 chia th\u00e0nh c\u00e1c nh\u00f3m b\u1eb1ng nhau m\u00e0 kh\u00f4ng b\u1ecb d\u01b0.<\/span><\/li>\n
          • L\u1eadp l\u1ecbch cho c\u00e1c ho\u1ea1t \u0111\u1ed9ng \u0111\u1ecbnh k\u1ef3: Trong th\u1ef1c t\u1ebf, BCNN \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh th\u1eddi \u0111i\u1ec3m c\u00e1c c\u00f4ng vi\u1ec7c ho\u1eb7c s\u1ef1 ki\u1ec7n di\u1ec5n ra \u0111\u1ed3ng th\u1eddi theo chu k\u1ef3.<\/span><\/li>\n<\/ul>\n

            \"boi-so-4\"<\/p>\n

            C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 b\u1ed9i s\u1ed1<\/b><\/h2>\n

            B\u1ed9i s\u1ed1 l\u00e0 g\u00ec?<\/b><\/h3>\n

            L\u00e0 s\u1ed1 t\u1ef1 nhi\u00ean chia h\u1ebft cho m\u1ed9t s\u1ed1 cho tr\u01b0\u1edbc; n\u1ebfu b chia h\u1ebft cho a th\u00ec b l\u00e0 b\u1ed9i c\u1ee7a a.<\/span><\/p>\n

            C\u00e1ch t\u00ecm b\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1?<\/b><\/h3>\n

            Nh\u00e2n s\u1ed1 \u0111\u00f3 l\u1ea7n l\u01b0\u1ee3t v\u1edbi 0, 1, 2, 3\u2026 \u0111\u1ec3 \u0111\u01b0\u1ee3c c\u00e1c b\u1ed9i.<\/span><\/p>\n

            M\u1ed9t s\u1ed1 c\u00f3 bao nhi\u00eau b\u1ed9i?<\/b><\/h3>\n

            C\u00f3 v\u00f4 s\u1ed1 b\u1ed9i, v\u00ec c\u00f3 th\u1ec3 nh\u00e2n v\u1edbi v\u00f4 s\u1ed1 s\u1ed1 t\u1ef1 nhi\u00ean.<\/span><\/p>\n

            B\u1ed9i chung nh\u1ecf nh\u1ea5t l\u00e0 g\u00ec?<\/b><\/h3>\n

            L\u00e0 s\u1ed1 nh\u1ecf nh\u1ea5t kh\u00e1c 0 trong c\u00e1c b\u1ed9i chung c\u1ee7a hai hay nhi\u1ec1u s\u1ed1.<\/span><\/p>\n

            \u01af\u1edbc v\u00e0 b\u1ed9i kh\u00e1c nhau th\u1ebf n\u00e0o?<\/b><\/h3>\n

            M\u1ed9t s\u1ed1 c\u00f3 h\u1eefu h\u1ea1n \u01b0\u1edbc nh\u01b0ng c\u00f3 v\u00f4 s\u1ed1 b\u1ed9i; n\u1ebfu a chia h\u1ebft cho b th\u00ec b l\u00e0 \u01b0\u1edbc, a l\u00e0 b\u1ed9i.<\/span><\/p>\n

            K\u1ebft lu\u1eadn<\/b><\/h2>\n

            B\u1ed9i s\u1ed1 l\u00e0 g\u00ec? <\/b>T\u00f3m l\u1ea1i, b\u1ed9i c\u1ee7a a l\u00e0 c\u00e1c s\u1ed1 chia h\u1ebft cho a (0, a, 2a, 3a\u2026); m\u1ed9t s\u1ed1 c\u00f3 v\u00f4 s\u1ed1 b\u1ed9i, v\u00e0 BCNN l\u00e0 b\u1ed9i chung nh\u1ecf nh\u1ea5t kh\u00e1c 0. N\u1eafm v\u1eefng b\u1ed9i s\u1ed1 c\u00f9ng quan h\u1ec7 \u01b0\u1edbc \u2013 b\u1ed9i gi\u00fap b\u1ea1n h\u1ecdc t\u1ed1t ph\u1ea7n chia h\u1ebft v\u00e0 ph\u00e2n s\u1ed1. \u0110\u1ec3 h\u1ecdc th\u00eam, m\u1eddi b\u1ea1n tham kh\u1ea3o c\u00e1c b\u00e0i<\/span> t\u1eadp h\u1ee3p s\u1ed1 nguy\u00ean Z l\u00e0 g\u00ec<\/span><\/a>,<\/span> kh\u00e1i ni\u1ec7m v\u00e0 \u1ee9ng d\u1ee5ng c\u1ee7a s\u1ed1 nguy\u00ean<\/span><\/a> v\u00e0<\/span> c\u00f4ng th\u1ee9c t\u1ed5 h\u1ee3p, ch\u1ec9nh h\u1ee3p<\/span><\/a> tr\u00ean chuy\u00ean m\u1ee5c tin t\u1ee9c c\u1ee7a Ho\u00e0ng H\u00e0 Mobile.\u00a0<\/span><\/p>\n

            Xem th\u00eam:<\/b><\/p>\n

              \n
            • \n

              C\u00f4ng Th\u1ee9c T\u00ednh Qu\u00e3ng \u0110\u01b0\u1eddng: C\u00e1ch T\u00ednh To\u00e1n L\u1edbp 5 & V\u1eadt L\u00fd L\u1edbp 8<\/a><\/p>\n<\/li>\n

            • \n

              Th\u1ec3 t\u00edch h\u00ecnh h\u1ed9p ch\u1eef nh\u1eadt: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i<\/a><\/p>\n<\/li>\n<\/ul>\n