{"id":12,"date":"2022-04-12T11:48:58","date_gmt":"2022-04-12T11:48:58","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=12"},"modified":"2025-08-04T05:50:11","modified_gmt":"2025-08-04T05:50:11","slug":"a-2-divisibility-rules","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/a-2-divisibility-rules\/","title":{"rendered":"A.2 Divisibility rules"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Divisibility rules<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Class-7-A.4-__Divisibility-rules__.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-869a5c0b6b78055316c8d0186252dcbd\" style=\"color:#74008b\"><strong>key notes :<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-normal-font-size wp-elements-fa8e69ce8e6fd2869a4892536c46372b\" style=\"color:#000060\"><strong>Divisibility by 2<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 2<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li class=\"has-normal-font-size\"><strong>Rule<\/strong>: A number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8.<\/li>\n\n\n\n<li><strong>Example<\/strong>: 24 is divisible by 2 because it ends in 4.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 3<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 3 if the sum of its digits is divisible by 3.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For 123, the sum of the digits is 1 + 2 + 3 = 6, which is divisible by 3.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by <strong>4<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 4 if the number formed by the last two digits is divisible by 4.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For 312, the last two digits are 12, and 12 is divisible by 4.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 5<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 5 if its last digit is 0 or 5.<\/li>\n\n\n\n<li><strong>Example<\/strong>: 45 is divisible by 5 because it ends in 5.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 6<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 6 if it is divisible by both 2 and 3.<\/li>\n\n\n\n<li><strong>Example<\/strong>: 18 is divisible by 6 because it\u2019s even (divisible by 2) and the sum of digits (1+8=9) is divisible by 3.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 7<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: Double the last digit and subtract it from the rest of the number. If the result is divisible by 7 (including 0), then the original number is divisible by 7.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For 203, double the last digit (6), subtract from the rest (20 &#8211; 6 = 14), and since 14 is divisible by 7, so is 203.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 8<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 8 if the number formed by the last three digits is divisible by 8.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For 1,856, the last three digits are 856, and 856 is divisible by 8.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 9<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 9 if the sum of its digits is divisible by 9.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For 729, the sum of the digits is 7 + 2 + 9 = 18, and 18 is divisible by 9.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 10<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 10 if its last digit is 0.<\/li>\n\n\n\n<li><strong>Example<\/strong>: 50 is divisible by 10 because it ends in 0.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 11<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For 2728, sum of digits in odd positions (2 + 2 = 4) and sum of digits in even positions (7 + 8 = 15), difference is |4 &#8211; 15| = 11, which is divisible by 11.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Divisibility by 12<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Rule<\/strong>: A number is divisible by 12 if it is divisible by both 3 and 4.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For 144, since 144 is divisible by 3 (sum of digits is 9) and 4 (last two digits 44 are divisible by 4), it is divisible by 12.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Tips for Students<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Practice<\/strong>: Use these rules to check your work and solve problems.<\/li>\n\n\n\n<li><strong>Patterns<\/strong>: Look for patterns in the rules to help remember them.<\/li>\n\n\n\n<li><strong>Examples<\/strong>: Work through several examples to see how the rules work.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Learn with an example<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-e7ce361eb9ca0477934e3ff942e7d4c4\" style=\"background-color:#a3e0fb\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-e64a46955050dc75a348fdb82ed2e687\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color has-normal-font-size wp-elements-89a003866f0501256e7fa22f2d0e4265\" style=\"color:#b00012\"><strong> \ud83d\ude00 Is 84,410,298 divisible by 5?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-normal-font-size\">Try the &#8220;divisible by 5&#8221; rule on 84,410,298.<\/p>\n\n\n\n<p>Look at the ones digit:<\/p>\n\n\n\n<p>84,410,298<\/p>\n\n\n\n<p>The ones digit is 8.&nbsp;<\/p>\n\n\n\n<p>The rule says that 84,410,298 is not divisible by 5.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-83f24f96df2965c311f360b8ba593686\" style=\"background-color:#89f9bd\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-148449d009637c5cceb3500ca384da58\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-81bf044c5862e7a162603f3ff0327d90\" style=\"color:#b00012\"><strong> \ud83d\ude00  Is 37,770,710 divisible by 10?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Try the &#8220;divisible by 10&#8221; rule on 37,770,710.<\/p>\n\n\n\n<p>Look at the ones digit:<\/p>\n\n\n\n<p>37,770,710<\/p>\n\n\n\n<p>The ones digit is 0.&nbsp;<\/p>\n\n\n\n<p>The rule says that 37,770,710 is divisible by 10.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-normal-font-size wp-elements-e963dabcd1f2b95779b8d0fffe9f348e\" style=\"background-color:#c9cff8\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-cb686497d20a91e6ded916abd8d1d346\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-59099d102569936b92dda9583b81f9c9\" style=\"color:#b00012\"><strong> \ud83d\ude00  Is 8,611,390 divisible by 2?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Try the &#8220;divisible by 2&#8221; rule on 8,611,390.<\/p>\n\n\n\n<p>Look at the ones digit:<\/p>\n\n\n\n<p>8,611,390<\/p>\n\n\n\n<p>The ones digit is 0.&nbsp;<\/p>\n\n\n\n<p>The rule says that 8,611,390 is divisible by 2.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/95322\/818\/926\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-6.png\" alt=\"\" class=\"wp-image-8432\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-6.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-6-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-6-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/31271\/165\/377\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-6.png\" alt=\"\" class=\"wp-image-8433\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-6.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-6-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-6-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Divisibility rules key notes : Divisibility by 2 Divisibility by 2 Divisibility by 3 Divisibility by 4 Divisibility by 5 Divisibility by 6 Divisibility by 7 Divisibility by 8 Divisibility by 9 Divisibility by 10 Divisibility by 11 Divisibility by 12 Tips for Students Learn with an example \ud83d\ude00 Is 84,410,298 divisible by 5? Try<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/a-2-divisibility-rules\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.2 Divisibility rules&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-12","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/12","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=12"}],"version-history":[{"count":27,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/12\/revisions"}],"predecessor-version":[{"id":20967,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/12\/revisions\/20967"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=12"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}