{"id":13,"date":"2022-04-12T08:45:13","date_gmt":"2022-04-12T08:45:13","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=13"},"modified":"2025-08-19T17:57:37","modified_gmt":"2025-08-19T17:57:37","slug":"a-2-prime-factorisation","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/a-2-prime-factorisation\/","title":{"rendered":"A.2 Prime factorisation"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Prime factorisation<\/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\/DAGv3Eqo-Mo\/Z4ea8-GRcdXEiQKEIssX4g\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGv3Eqo-Mo&#x2F;Z4ea8-GRcdXEiQKEIssX4g&#x2F;watch?utm_content=DAGv3Eqo-Mo&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">7th class &#8211; PRIME FACTORISATION<\/a> by Delta publications\n<\/div>\n<\/div>\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 Prime Factorisation?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Prime Factorisation<\/strong> is the process of breaking down a number into the set of prime numbers that, when multiplied together, give the original number.<\/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>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><strong>Prime Numbers:<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-normal-font-size\"><strong>Definition:<\/strong> Numbers greater than 1 that have exactly two factors: 1 and themselves.<\/li>\n\n\n\n<li><strong>Examples:<\/strong> 2, 3, 5, 7, 11, 13, 17, etc.<\/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><strong>Composite Numbers:<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition:<\/strong> Numbers that have more than two factors.<\/li>\n\n\n\n<li><strong>Examples:<\/strong> 4, 6, 8, 9, 10, 12, etc.<\/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>Factors:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Definition:<\/strong> Numbers that divide another number exactly (without leaving a remainder).<\/li>\n\n\n\n<li><strong>Example:<\/strong> Factors of 12 are 1, 2, 3, 4, 6, 12.<\/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>How to Find Prime Factorisation<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Start with the Number:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Choose a number you want to factorise.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Divide by the Smallest Prime Number:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Divide the number by the smallest prime number (2) if possible.<\/li>\n\n\n\n<li>If not, move to the next smallest prime number (3), and so on.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Continue Until the Quotient is a Prime Number:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Keep dividing by the smallest prime number until you are left with 1.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Write Down the Prime Factors:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>List all the prime numbers you used to divide the original number.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Express as a Product:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Write the number as the product of its prime factors.<\/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>Example:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#b3b1f4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-tertiary-background-color has-background\"><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-c21f28b2c7ff113d46839070e9023e2f\" style=\"color:#f64444\"><strong>Find the Prime Factorisation of 36<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Start with 36.<\/strong><\/li>\n\n\n\n<li><strong>Divide by 2 (the smallest prime number):<\/strong> 36\u00f72=18<\/li>\n\n\n\n<li><strong>Divide 18 by 2:<\/strong> 18\u00f72=9<\/li>\n\n\n\n<li><strong>Divide 9 by 3 (next smallest prime number):<\/strong> 9\u00f73=3<\/li>\n\n\n\n<li><strong>Divide 3 by 3:<\/strong> 3\u00f73=1<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>So the prime factorisation of 36 is 2\u00b2\u00d73\u00b2.<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code has-background-background-color has-background has-normal-font-size\"><code>  36\n \/  \\\n2    18\n    \/  \\\n   2    9\n       \/  \\\n      3    3<\/code><\/pre>\n\n\n\n<p class=\"has-normal-font-size\">From the factor tree, you can see that 36 = 2 \u00d7 2 \u00d7 3 \u00d7 3, <strong>2\u00b2\u00d73\u00b2<\/strong>.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#b5f3bc\"><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-background-background-color has-text-color has-background has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Why Prime Factorisation is Useful<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Simplifying Fractions:<\/strong><\/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<ul class=\"wp-block-list\">\n<li>Helps in finding the greatest common divisor.<\/li>\n<\/ul>\n\n\n\n<p><strong>Finding LCM and GCD:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Useful in problems involving least common multiple (LCM) and greatest common divisor (GCD).<\/li>\n<\/ul>\n\n\n\n<p><strong>Understanding Number Properties:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Helps in learning about number divisibility and properties.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#75f8f8\"><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>Practice Problems<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li class=\"has-normal-font-size\">Find the prime factorisation of 30.<\/li>\n\n\n\n<li class=\"has-normal-font-size\">Find the prime factorisation of 56.<\/li>\n\n\n\n<li class=\"has-normal-font-size\">Write 45 as a product of prime factors.<\/li>\n<\/ol>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>let&#8217;s practice!<\/strong><\/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\/34594\/317\/151\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-1.png\" alt=\"\" class=\"wp-image-6465\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-1.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-1-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-1-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-1-400x400.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\/468\/170\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-1.png\" alt=\"\" class=\"wp-image-6466\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-1.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-1-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-1-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-1-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Prime factorisation 7th class &#8211; PRIME FACTORISATION by Delta publications Key Notes: What is Prime Factorisation? Prime Factorisation is the process of breaking down a number into the set of prime numbers that, when multiplied together, give the original number. Key Concepts Prime Numbers: Composite Numbers: Factors: How to Find Prime Factorisation Start with the<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/a-2-prime-factorisation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.2 Prime factorisation&#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-13","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/13","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=13"}],"version-history":[{"count":32,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/13\/revisions"}],"predecessor-version":[{"id":16791,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/13\/revisions\/16791"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=13"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}