{"id":27152,"date":"2023-09-07T20:25:52","date_gmt":"2023-09-07T13:25:52","guid":{"rendered":"https:\/\/ungdung.hotronghiencuu.com\/open\/boi-so-la-gi-2"},"modified":"2023-09-07T20:25:52","modified_gmt":"2023-09-07T13:25:52","slug":"boi-so-la-gi-2","status":"publish","type":"post","link":"https:\/\/ungdung.hotronghiencuu.com\/open\/boi-so-la-gi-2","title":{"rendered":"B\u1ed9i s\u1ed1 l\u00e0 g\u00ec? T\u00ecm hi\u1ec3u kh\u00e1i ni\u1ec7m v\u00e0 v\u00ed d\u1ee5 v\u1ec1 b\u1ed9i s\u1ed1"},"content":{"rendered":"<p>&#8220;B\u1ed9i s\u1ed1 l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong to\u00e1n h\u1ecdc, \u0111\u1ea1i di\u1ec7n cho k\u1ebft qu\u1ea3 c\u1ee7a vi\u1ec7c nh\u00e2n hai ho\u1eb7c nhi\u1ec1u s\u1ed1 l\u1ea1i v\u1edbi nhau. B\u1ed9i s\u1ed1 c\u00f3 th\u1ec3 gi\u00fap ch\u00fang ta t\u00ednh to\u00e1n nhanh ch\u00f3ng v\u00e0 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c s\u1ed1. H\u00e3y c\u00f9ng kh\u00e1m ph\u00e1 v\u00e0 t\u00ecm hi\u1ec3u v\u1ec1 b\u1ed9i s\u1ed1 l\u00e0 g\u00ec qua b\u00e0i vi\u1ebft n\u00e0y.&#8221;<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_40 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-6ace6e4218da1\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-6ace6e4218da1\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/boi-so-la-gi-2\/#Boi_so_la_gi_Cach_tim_boi_cua_mot_so_bat_ky\" title=\"B\u1ed9i s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch t\u00ecm b\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3\">B\u1ed9i s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch t\u00ecm b\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/boi-so-la-gi-2\/#Vi_du\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/boi-so-la-gi-2\/#Bai_tap_luyen_tap\" title=\"B\u00e0i t\u1eadp luy\u1ec7n t\u1eadp:\">B\u00e0i t\u1eadp luy\u1ec7n t\u1eadp:<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/boi-so-la-gi-2\/#a_Tim_cac_boi_be_hon_20_cua_so_2\" title=\"a) T\u00ecm c\u00e1c b\u1ed9i b\u00e9 h\u01a1n 20 c\u1ee7a s\u1ed1 2:\">a) T\u00ecm c\u00e1c b\u1ed9i b\u00e9 h\u01a1n 20 c\u1ee7a s\u1ed1 2:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/boi-so-la-gi-2\/#b_Tim_cac_boi_be_hon_25_cua_so_3\" title=\"b) T\u00ecm c\u00e1c b\u1ed9i b\u00e9 h\u01a1n 25 c\u1ee7a s\u1ed1 3:\">b) T\u00ecm c\u00e1c b\u1ed9i b\u00e9 h\u01a1n 25 c\u1ee7a s\u1ed1 3:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/boi-so-la-gi-2\/#c_Tim_boi_chung_nho_nhat_cua_5_va_7\" title=\"c) T\u00ecm b\u1ed9i chung nh\u1ecf nh\u1ea5t c\u1ee7a 5 v\u00e0 7:\">c) T\u00ecm b\u1ed9i chung nh\u1ecf nh\u1ea5t c\u1ee7a 5 v\u00e0 7:<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Boi_so_la_gi_Cach_tim_boi_cua_mot_so_bat_ky\"><\/span>B\u1ed9i s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch t\u00ecm b\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"B\u1ed9i s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch t\u00ecm b\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/boi_so_la_gi_tim_hieu_khai_niem_va_vi_du_ve_boi_so-1.jpeg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"B\u1ed9i s\u1ed1 l\u00e0 g\u00ec? C\u00e1ch t\u00ecm b\u1ed9i c\u1ee7a m\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3\"\/><\/p>\n<p>B\u1ed9i s\u1ed1 l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong to\u00e1n h\u1ecdc. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ch\u1ec9 m\u1ed9t s\u1ed1 nguy\u00ean d\u01b0\u01a1ng \u0111\u01b0\u1ee3c nh\u00e2n v\u1edbi m\u1ed9t s\u1ed1 kh\u00e1c \u0111\u1ec3 thu \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean d\u01b0\u01a1ng kh\u00e1c. \u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 b\u1ed9i s\u1ed1, ch\u00fang ta h\u00e3y x\u00e9t v\u00ed d\u1ee5 sau.<\/p>\n<p>Cho hai s\u1ed1 t\u1ef1 nhi\u00ean a v\u00e0 b, khi a chia h\u1ebft cho b (khi ph\u00e9p chia a\/b c\u00f3 k\u1ebft qu\u1ea3 l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean), ta n\u00f3i a l\u00e0 b\u1ed9i c\u1ee7a b. V\u00ed d\u1ee5, 12 chia h\u1ebft cho 3 (12\/3 = 4), v\u1eady 12 l\u00e0 b\u1ed9i c\u1ee7a 3. T\u01b0\u01a1ng t\u1ef1, 15 c\u0169ng l\u00e0 b\u1ed9i c\u1ee7a 3 v\u00ec 15 chia h\u1ebft cho 3 (15\/3 = 5).<\/p>\n<p>\u0110\u1ec3 t\u00ecm c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a m\u1ed9t s\u1ed1 b\u1ea5t k\u1ef3, ta th\u1ef1c hi\u1ec7n vi\u1ec7c nh\u00e2n s\u1ed1 \u0111\u00f3 l\u1ea7n l\u01b0\u1ee3t v\u1edbi c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 0 tr\u1edf \u0111i. Khi \u0111\u00f3, c\u00e1c k\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c \u0111\u1ec1u l\u00e0 c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a s\u1ed1 \u0111\u00f3. V\u00ed d\u1ee5, \u0111\u1ec3 t\u00ecm c\u00e1c b\u1ed9i c\u1ee7a 4, ta nh\u00e2n 4 l\u1ea7n l\u01b0\u1ee3t v\u1edbi c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 0:<br \/>\n0 x 4 = 0,<br \/>\n1 x 4 = 4,<br \/>\n2 x 4 = 8,<br \/>\n3 x 4 = 12,<br \/>\nv\u00e0 c\u1ee9 ti\u1ebfp t\u1ee5c nh\u01b0 v\u1eady. C\u00e1c k\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c l\u00e0 c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a s\u1ed1 4.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Vi_du\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>&#8211; B\u1ed9i s\u1ed1 c\u1ee7a 4 l\u00e0: 0, 4, 8, 12,&#8230;<br \/>\n&#8211; B\u1ed9i s\u1ed1 c\u1ee7a 3 l\u00e0: 0, 3, 6, 9,&#8230;<br \/>\n&#8211; B\u1ed9i s\u1ed1 c\u1ee7a 5 l\u00e0: 0,5,10,15,&#8230;<\/p>\n<p>T\u1eeb v\u00ed d\u1ee5 tr\u00ean, ta c\u00f3 th\u1ec3 th\u1ea5y r\u1eb1ng m\u1ed7i s\u1ed1 t\u1ef1 nhi\u00ean \u0111\u1ec1u c\u00f3 v\u00f4 h\u1ea1n b\u1ed9i s\u1ed1. Ngo\u00e0i ra, m\u1ed7i s\u1ed1 c\u0169ng ch\u1ee9a ch\u00ednh n\u00f3 trong c\u00e1c b\u1ed9i s\u1ed1 c\u1ee7a n\u00f3.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Bai_tap_luyen_tap\"><\/span>B\u00e0i t\u1eadp luy\u1ec7n t\u1eadp:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"B\u00e0i t\u1eadp luy\u1ec7n t\u1eadp:\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/boi_so_la_gi_tim_hieu_khai_niem_va_vi_du_ve_boi_so-2.jpeg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"B\u00e0i t\u1eadp luy\u1ec7n t\u1eadp:\"\/><\/p>\n<p>\u0110\u1ec3 r\u00e8n k\u1ef9 n\u0103ng trong vi\u1ec7c t\u00ecm b\u1ed9i s\u1ed1 c\u1ee7a m\u1ed9t s\u1ed1 \u0111\u00e3 cho, ch\u00fang ta c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n c\u00e1c b\u00e0i t\u1eadp sau:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"a_Tim_cac_boi_be_hon_20_cua_so_2\"><\/span>a) T\u00ecm c\u00e1c b\u1ed9i b\u00e9 h\u01a1n 20 c\u1ee7a s\u1ed1 2:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>&#8211; S\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p nh\u00e2n l\u1ea7n l\u01b0\u1ee3t v\u1edbi c\u00e1c s\u1ed1 t\u1eeb t\u1ef1 nhi\u00ean t\u1eeb 0 tr\u1edf \u0111i.<br \/>\n&#8211; K\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c:<br \/>\n    + B\u1ed9i c\u1ee7a s\u1ed1 2 b\u00e9 h\u01a1n ho\u1eb7c b\u1eb1ng14 l\u00e0:0,2,4,6,8,10,12<br \/>\n    + B\u1ed9i c\u1ee7a s\u1ed1 b\u00e9 h\u01a1n 20 l\u00e0:0,2,4,6,8,10,12, 14, 16, 18<br \/>\n&#8211; V\u1eady c\u00e1c b\u1ed9i s\u1ed1 b\u00e9 h\u01a1n 20 c\u1ee7a s\u1ed1 2 l\u00e0: 0,2,4,6,8,10,12,14.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"b_Tim_cac_boi_be_hon_25_cua_so_3\"><\/span>b) T\u00ecm c\u00e1c b\u1ed9i b\u00e9 h\u01a1n 25 c\u1ee7a s\u1ed1 3:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>&#8211; S\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p nh\u00e2n l\u1ea7n l\u01b0\u1ee3t v\u1edbi c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean t\u1eeb 0 tr\u1edf \u0111i.<br \/>\n&#8211; K\u1ebft qu\u1ea3 thu \u0111\u01b0\u1ee3c:<br \/>\n    + B\u1ed9i c\u1ee7a s\u1ed1 b\u00e9 h\u01a1n ho\u1eb7c b\u1eb1ng21 l\u00e0 :0,3,6,9,12,15,18<br \/>\n    + B\u1ed9i c\u1ee7a s\u1ed1 b\u00e9 h\u01a1n 25 l\u00e0:0,3,6,,9,,12,,15,,18,,21<\/p>\n<p>V\u1eady c\u00e1c b\u1ed9i s\u1ed1 b\u00e9 h\u01a1n25 c\u1ee7a s\u1ed13 l\u00e0:0,3,6,,9,,12,,15,,18,,21.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"c_Tim_boi_chung_nho_nhat_cua_5_va_7\"><\/span>c) T\u00ecm b\u1ed9i chung nh\u1ecf nh\u1ea5t c\u1ee7a 5 v\u00e0 7:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>&#8211; S\u1eed d\u1ee5ng ph\u01b0\u01a1ng ph\u00e1p t\u00ecm b\u1ed9i chung nh\u1ecf nh\u1ea5t.<br \/>\n&#8211; C\u00e1c b\u1ed9i c\u1ee7a5:&#8230;,-10,-5,,,0,,,,5,,,,10,,,,15,,,20&#8230;.<br \/>\n&#8211; C\u00e1c b\u1ed9i c\u1ee7a7:&#8230;,-21,-14,,, -7,,,0,,,,7,,,,14,,,,21,,,28&#8230;.<br \/>\n&#8211; Nh\u1eadn x\u00e9t ta th\u1ea5y k\u1ebft qu\u1ea3 \u0111\u1ea7u ti\u00ean chung gi\u1eefa hai chu\u1ed7i tr\u00ean l\u1ea1i l\u00e035.<br \/>\n   V\u1eady ta c\u00f3 \u0111\u01b0\u1ee3c : B\u1ed9i chung nh\u1ecf nh\u1ea5t c\u1ee7a5 v\u00e07l\u00e035.<\/p>\n<p>B\u1ed9i s\u1ed1 l\u00e0 k\u1ebft qu\u1ea3 c\u1ee7a ph\u00e9p nh\u00e2n hai s\u1ed1 nguy\u00ean, \u0111\u1ea1i di\u1ec7n cho s\u1ed1 l\u1ea7n m\u00e0 m\u1ed9t s\u1ed1 chia h\u1ebft cho s\u1ed1 kh\u00e1c. \u0110\u00e2y l\u00e0 kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 c\u00f3 \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y, t\u1eeb t\u00ednh to\u00e1n t\u00e0i ch\u00ednh \u0111\u1ebfn x\u00e2y d\u1ef1ng c\u00f4ng tr\u00ecnh. Hi\u1ec3u v\u1ec1 b\u1ed9i s\u1ed1 gi\u00fap ta hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 s\u1ef1 t\u01b0\u01a1ng quan gi\u1eefa c\u00e1c s\u1ed1 v\u00e0 \u00e1p d\u1ee5ng v\u00e0o c\u00e1c v\u1ea5n \u0111\u1ec1 th\u1ef1c t\u1ebf.<br \/>\n<iframe loading=\"lazy\" title=\"B\u1ed9i s\u1ed1 l\u00e0 g\u00ec v\u00ed d\u1ee5 | to\u00e1n l\u1edbp 6\" width=\"790\" height=\"444\" src=\"https:\/\/www.youtube.com\/embed\/jk5F3vb9ogg?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>&#8220;B\u1ed9i s\u1ed1 l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong to\u00e1n h\u1ecdc, \u0111\u1ea1i di\u1ec7n cho k\u1ebft qu\u1ea3 c\u1ee7a vi\u1ec7c nh\u00e2n hai ho\u1eb7c nhi\u1ec1u s\u1ed1 l\u1ea1i v\u1edbi nhau. B\u1ed9i&#8230; <\/p>\n","protected":false},"author":1,"featured_media":27150,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-27152","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-khai-niem-1"],"_links":{"self":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/27152","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/comments?post=27152"}],"version-history":[{"count":0,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/27152\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media\/27150"}],"wp:attachment":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media?parent=27152"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/categories?post=27152"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/tags?post=27152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}