{"id":17,"date":"2022-04-12T08:46:02","date_gmt":"2022-04-12T08:46:02","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=17"},"modified":"2025-07-29T09:40:12","modified_gmt":"2025-07-29T09:40:12","slug":"a-4-divisibility-rules","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/a-4-divisibility-rules\/","title":{"rendered":"A.4 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:\/\/7thclass.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-huge-font-size\" style=\"color:#74008b\">Key Notes:<\/p>\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>What are Divisibility Rules?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">Divisibility rules are shortcuts to help you figure out if a number can be divided evenly by another number without actually doing the division. They&#8217;re super useful for simplifying fractions, solving problems, and understanding numbers better! Let&#8217;s explore some common divisibility rules.<\/p>\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>Divisibility by 2<\/strong><\/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>: <\/li>\n\n\n\n<li>24 is divisible by 2 because it ends in 4.<\/li>\n\n\n\n<li>12 is divisible by 2 because its last digit is 2.<\/li>\n\n\n\n<li>346 is divisible by 2 because its last digit is 6.<\/li>\n\n\n\n<li>1000 is divisible by 2 because its last digit is 0.<\/li>\n\n\n\n<li>23 is <strong>not<\/strong> divisible by 2 because its last digit is 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><strong>Divisibility by 3<\/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 3 if the sum of its digits is divisible by 3.<\/li>\n\n\n\n<li><strong>Example<\/strong>: <\/li>\n\n\n\n<li>123 is divisible by 3 because 1 + 2 + 3 = 6, and 6 is divisible by 3.<\/li>\n\n\n\n<li>456 is divisible by 3 because 4 + 5 + 6 = 15, and 15 is divisible by 3.<\/li>\n\n\n\n<li>78 is divisible by 3 because 7 + 8 = 15, and 15 is divisible by 3.<\/li>\n\n\n\n<li>100 is <strong>not<\/strong> divisible by 3 because 1 + 0 + 0 = 1, and 1 is not 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><strong>Divisibility by 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>: <\/li>\n\n\n\n<li>For 312, the last two digits are 12, and 12 is divisible by 4.<\/li>\n\n\n\n<li>112 is divisible by 4 because 12 is divisible by 4.<\/li>\n\n\n\n<li>324 is divisible by 4 because 24 is divisible by 4.<\/li>\n\n\n\n<li>1600 is divisible by 4 because 00 is divisible by 4.<\/li>\n\n\n\n<li>210 is <strong>not<\/strong> divisible by 4 because 10 is not 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><strong>Divisibility by 5<\/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 5 if its last digit is 0 or 5.<\/li>\n\n\n\n<li><strong>Example<\/strong>: <\/li>\n\n\n\n<li>45 is divisible by 5 because it ends in 5.<\/li>\n\n\n\n<li>25 is divisible by 5 because its last digit is 5.<\/li>\n\n\n\n<li>130 is divisible by 5 because its last digit is 0.<\/li>\n\n\n\n<li>1000 is divisible by 5 because its last digit is 0.<\/li>\n\n\n\n<li>12 is <strong>not<\/strong> divisible by 5 because its last digit is 2.<\/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>Divisibility by 6<\/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 6 if it is divisible by both 2 and 3.<\/li>\n\n\n\n<li><strong>Example<\/strong>: <\/li>\n\n\n\n<li>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\n\n\n<li>24 is divisible by 6 because it&#8217;s even (divisible by 2) and 2 + 4 = 6 (divisible by 3).<\/li>\n\n\n\n<li>132 is divisible by 6 because it&#8217;s even (divisible by 2) and 1 + 3 + 2 = 6 (divisible by 3).<\/li>\n\n\n\n<li>12 is divisible by 6 because it&#8217;s even (divisible by 2) and 1 + 2 = 3 (divisible by 3).<\/li>\n\n\n\n<li>25 is <strong>not<\/strong> divisible by 6 because although it is not divisible by 2, it is not 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><strong>Divisibility by 7<\/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>: 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><strong>Divisibility by 8<\/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 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><strong>Divisibility by 9<\/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 9 if the sum of its digits is divisible by 9.<\/li>\n\n\n\n<li><strong>Example<\/strong>: <\/li>\n\n\n\n<li>For 729, the sum of the digits is 7 + 2 + 9 = 18, and 18 is divisible by 9.<\/li>\n\n\n\n<li>81 is divisible by 9 because 8 + 1 = 9, and 9 is divisible by 9.<\/li>\n\n\n\n<li>279 is divisible by 9 because 2 + 7 + 9 = 18, and 18 is divisible by 9.<\/li>\n\n\n\n<li>999 is divisible by 9 because 9 + 9 + 9 = 27, and 27 is divisible by 9.<\/li>\n\n\n\n<li>100 is <strong>not<\/strong> divisible by 9 because 1 + 0 + 0 = 1, and 1 is not 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><strong>Divisibility by 10<\/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 10 if its last digit is 0.<\/li>\n\n\n\n<li><strong>Example<\/strong>:<\/li>\n\n\n\n<li>50 is divisible by 10 because its last digit is 0.<\/li>\n\n\n\n<li>230 is divisible by 10 because its last digit is 0.<\/li>\n\n\n\n<li>1000 is divisible by 10 because its last digit is 0.<\/li>\n\n\n\n<li>45 is <strong>not<\/strong> divisible by 10 because its last digit is 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><strong>Divisibility by 11<\/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 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><strong>Divisibility by 12<\/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 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<div class=\"wp-block-group has-background\" style=\"background-color:#f1b2e3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading has-background-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-2c5d9626ae0dc67ddee5a58969ec5bb7\" style=\"color:#000060\"><strong>Tips for Students<\/strong><\/h3>\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\n\n\n<li><strong>2:<\/strong> Last digit is even (0, 2, 4, 6, 8).<\/li>\n\n\n\n<li><strong>3:<\/strong> Sum of digits is divisible by 3.<\/li>\n\n\n\n<li><strong>4:<\/strong> The number formed by last 2 digits is divisible by 4<\/li>\n\n\n\n<li><strong>5:<\/strong> Last digit is 0 or 5.<\/li>\n\n\n\n<li><strong>6:<\/strong> Divisible by both 2 and 3.<\/li>\n\n\n\n<li><strong>9:<\/strong> Sum of digits is divisible by 9.<\/li>\n\n\n\n<li><strong>10:<\/strong> Last digit is 0.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\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-684b9a2cd3f62fa584887b26436bc324\" 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-f4968194968ea3d04abaee12ac624584\"><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-646d4b5e0c7cf7ccfa2c657f5d4b041c\" style=\"color:#b00012\"><strong> \ud83d\ude00 Is 84,410,298 divisible by 5?<\/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 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 class=\"has-normal-font-size\">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-large-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\/95278\/285\/902\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-3.png\" alt=\"\" class=\"wp-image-6473\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-3.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-3-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-3-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-3-400x400.png 400w\" 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\/75609\/983\/509\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-3.png\" alt=\"\" class=\"wp-image-6475\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-3.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-3-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-3-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-3-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Divisibility rules Key Notes: What are Divisibility Rules? Divisibility rules are shortcuts to help you figure out if a number can be divided evenly by another number without actually doing the division. They&#8217;re super useful for simplifying fractions, solving problems, and understanding numbers better! Let&#8217;s explore some common divisibility rules. Divisibility by 2 Divisibility by<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/a-4-divisibility-rules\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.4 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,"footnotes":""},"class_list":["post-17","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/17","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=17"}],"version-history":[{"count":28,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/17\/revisions"}],"predecessor-version":[{"id":16563,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/17\/revisions\/16563"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=17"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}