{"id":18,"date":"2022-04-12T11:50:01","date_gmt":"2022-04-12T11:50:01","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=18"},"modified":"2025-07-30T10:28:45","modified_gmt":"2025-07-30T10:28:45","slug":"a-5-highest-common-factor","status":"publish","type":"page","link":"https:\/\/8thclass.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<figure class=\"wp-block-video\"><video controls src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/A.5-Highest-common-factor.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<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<p><strong>Common Factor:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\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<p><strong>Highest Common Factor:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\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-large-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>1.<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>Find all the factors of each number.<\/p>\n\n\n\n<p><strong>Example:<\/strong> For 12 and 18:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Factors of 12: 1, 2, 3, 4, 6, 12<\/li>\n\n\n\n<li>Factors of 18: 1, 2, 3, 6, 9, 18<\/li>\n<\/ul>\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>2. 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>Break each number into prime factors.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>12 = 2\u00b2 \u00d7 3<\/li>\n\n\n\n<li>18 = 2 \u00d7 3\u00b2<\/li>\n<\/ul>\n\n\n\n<p><strong>Identify Common Prime Factors:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find the common prime factors.<\/li>\n\n\n\n<li><strong>Common Prime Factors:<\/strong> 2 and 3<\/li>\n<\/ul>\n\n\n\n<p><strong>Multiply the Lowest Powers:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\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>3. 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<p>Example: For 48 and 18:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\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\">\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\">\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<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<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#d5f9ca\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-background-background-color has-background has-normal-font-size\"><strong>Find the HCF of 24 and 36:<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Listing Factors:<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\">Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Common Factors:<\/strong> 1, 2, 3, 4, 6, <strong>12<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>HCF:<\/strong> 12<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Prime Factorisation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>24 = 2\u00b3 \u00d7 3<\/li>\n\n\n\n<li>36 = 2\u00b2 \u00d7 3\u00b2<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\">Common Prime Factors: 2\u00b2 \u00d73\u00b9 =12<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#f0d6f3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-background-background-color has-background has-normal-font-size\"><strong>Find the HCF of 56 and 84:<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Listing Factors:<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\">Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Common Factors:<\/strong> 1, 2, 4, 7, 14, <strong>28<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>HCF:<\/strong> 28<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Prime Factorisation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>56 = 2\u00b3 \u00d7 7<\/li>\n\n\n\n<li>84 = 2\u00b2 \u00d7 3 \u00d7 7<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\">Common Prime Factors: 2\u00b2 \u00d77\u00b9 =28<\/p>\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 has-normal-font-size\">\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 has-normal-font-size\">\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>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\" style=\"background-color:#aef1ef\"><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>Practice Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul 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<\/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>Visual Representation<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\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<p class=\"has-normal-font-size\"><strong>Prime Factorisation Example<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>12 = 2\u00b2 \u00d7 3 <\/li>\n\n\n\n<li>18 = 2 \u00d7 3\u00b2 <\/li>\n<\/ul>\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\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\/76680\/313\/216\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-3.png\" alt=\"\" class=\"wp-image-8423\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-3.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-3-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-3-150x150.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\/33788\/376\/938\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-3.png\" alt=\"\" class=\"wp-image-8424\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-3.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-3-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Highest common factor 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: How to Find the HCF There are different<a class=\"more-link\" href=\"https:\/\/8thclass.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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-18","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\/18","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=18"}],"version-history":[{"count":31,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/18\/revisions"}],"predecessor-version":[{"id":20955,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/18\/revisions\/20955"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=18"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}