{"id":19,"date":"2022-04-12T08:46:26","date_gmt":"2022-04-12T08:46:26","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=19"},"modified":"2025-08-19T18:00:21","modified_gmt":"2025-08-19T18:00:21","slug":"a-5-highest-common-factor","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/a-5-highest-common-factor\/","title":{"rendered":"A.5 Highest common factor"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Highest common factor<\/strong><\/h2>\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\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGv8OJBsnI\/BOQOWQicFTHIa5gAglJvtQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGv8OJBsnI&#x2F;BOQOWQicFTHIa5gAglJvtQ&#x2F;watch?utm_content=DAGv8OJBsnI&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">7th class &#8211; Highest common factor<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\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 is the Highest Common Factor?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Highest Common Factor (HCF)<\/strong>, also known as the <strong>Greatest Common Divisor (GCD)<\/strong>, is the largest number that can exactly divide two or more numbers without leaving a remainder.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Key Concepts<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\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>Common Factor:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Definition:<\/strong> A number that divides two or more numbers exactly.<\/li>\n\n\n\n<li><strong>Example:<\/strong> For 12 and 18, common factors are 1, 2, 3, 6.<\/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>Highest Common Factor:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Definition:<\/strong> The largest number that is a common factor of the given numbers.<\/li>\n\n\n\n<li><strong>Example:<\/strong> For 12 and 18, the HCF is 6.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>How to Find the HCF<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">There are different methods to find the HCF:<\/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>Listing Factors Method<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>List All Factors:<\/strong><\/p>\n\n\n\n<p><strong>Identify Common Factors:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find the numbers that appear in both lists.<\/li>\n\n\n\n<li><strong>Common Factors:<\/strong> 1, 2, 3, 6<\/li>\n<\/ul>\n\n\n\n<p><strong>Select the Greatest One:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The HCF is the largest number in the list of common factors.<\/li>\n\n\n\n<li><strong>HCF:<\/strong> 6<\/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>Prime Factorisation Method<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Prime Factorise Each Number:<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\">Break each number into prime factors.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>12 = 2\u00b2 \u00d7 3<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li>18 = 2 \u00d7 3\u00b2<\/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>Identify Common Prime Factors:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">Find the common prime factors.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Common Prime Factors:<\/strong> 2 and 3<\/p>\n\n\n\n<p><strong>Multiply the Lowest Powers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Multiply the common prime factors, using the smallest power for each prime.<\/li>\n\n\n\n<li><strong>HCF:<\/strong> 2\u00b9 \u00d7 3\u00b9 = 6<\/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>Euclidean Algorithm (for Advanced Students)<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Divide the Larger Number by the Smaller Number and Find the Remainder:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Example: For 48 and 18:<\/li>\n\n\n\n<li>48 \u00f7 18 = 2 remainder 12<\/li>\n<\/ul>\n\n\n\n<p><strong>Replace the Larger Number with the Smaller Number and the Smaller Number with the Remainder:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>New numbers: 18 and 12.<\/li>\n<\/ul>\n\n\n\n<p><strong>Repeat Until the Remainder is 0:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Continue the process until the remainder is 0.<\/li>\n\n\n\n<li>The divisor at this step is the HCF.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#ebb2e2\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\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>Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-background-background-color has-background\"><strong>Find the HCF of 24 and 36:<\/strong><\/p>\n\n\n\n<p><strong>Listing Factors:<\/strong><\/p>\n\n\n\n<p>Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24<\/p>\n\n\n\n<p>Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36<\/p>\n\n\n\n<p><strong>Common Factors:<\/strong> 1, 2, 3, 4, 6, <strong>12<\/strong><\/p>\n\n\n\n<p class=\"has-background-background-color has-background\"><strong>Find the HCF of 56 and 84:<\/strong><\/p>\n\n\n\n<p><strong>Listing Factors:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56<\/li>\n\n\n\n<li>Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84<\/li>\n\n\n\n<li><strong>Common Factors:<\/strong> 1, 2, 4, 7, 14, <strong>28<\/strong><\/li>\n\n\n\n<li><strong>HCF:<\/strong> 28<strong>Prime Factorisation:<\/strong><\/li>\n\n\n\n<li>56 = 2\u00b3 \u00d7 7<\/li>\n\n\n\n<li>84 = 2\u00b2 \u00d7 3 \u00d7 7<\/li>\n\n\n\n<li>Common Prime Factors: 2\u00b2 \u00d77\u00b9 =28<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\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>Why HCF is Useful<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Simplifying Fractions:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-normal-font-size\">Helps in reducing fractions to their simplest form.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Solving Problems:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-normal-font-size\">Useful in problems related to grouping or arranging items.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Dividing Objects:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li class=\"has-normal-font-size\">Helps in dividing objects into equal parts without leftovers.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#6fe6f3\"><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-8848354e9f57fbad36d04a44f6a7dc2a\" style=\"color:#000060\"><strong>Practice Problems<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list has-normal-font-size\">\n<li>Find the HCF of 30 and 45.<\/li>\n\n\n\n<li>Find the HCF of 56 and 98.<\/li>\n\n\n\n<li>Find the HCF of 15 and 25.<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#adf4b2\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-background-background-color has-text-color has-background has-link-color has-normal-font-size wp-elements-41baac8d3cc3a4aea02ac165fd05fe75\" style=\"color:#000060\"><strong>Visual Representation<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code has-normal-font-size\"><code> 12: 1, 2, 3, 4, <strong>6<\/strong>, 12\n 18: 1, 2, 3, <strong>6<\/strong>, 9, 18<\/code><\/pre>\n\n\n\n<p class=\"has-normal-font-size\">Common Factors: 1, 2, 3, 6<br>Highest Common Factor: 6<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-normal-font-size\"><strong>Prime Factorisation Example<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\">12 = 2\u00b2 \u00d7 3 <\/p>\n\n\n\n<p class=\"has-normal-font-size\">18 = 2 \u00d7 3\u00b2 <\/p>\n\n\n\n<p class=\"has-normal-font-size\">Common Prime Factors: 2 and 3 <\/p>\n\n\n\n<p class=\"has-normal-font-size\">HCF = 2\u00b9 \u00d7 3\u00b9 = 6<\/p>\n<\/div><\/div>\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\/75641\/274\/256\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-4.png\" alt=\"\" class=\"wp-image-6477\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-4.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-4-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-4-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-4-400x400.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\/75610\/076\/377\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-4.png\" alt=\"\" class=\"wp-image-6479\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-4.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-4-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-4-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-4-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Highest common factor 7th class &#8211; Highest common factor by Delta publications Key Notes: What is the Highest Common Factor? Highest Common Factor (HCF), also known as the Greatest Common Divisor (GCD), is the largest number that can exactly divide two or more numbers without leaving a remainder. Key Concepts Common Factor: Highest Common Factor:<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/a-5-highest-common-factor\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.5 Highest common factor&#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-19","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/19","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=19"}],"version-history":[{"count":33,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":16794,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/19\/revisions\/16794"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}