{"id":19,"date":"2022-04-13T09:44:57","date_gmt":"2022-04-13T09:44:57","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=19"},"modified":"2025-08-04T07:01:17","modified_gmt":"2025-08-04T07:01:17","slug":"a-5-prime-factorisation","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/a-5-prime-factorisation\/","title":{"rendered":"A.5 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<figure class=\"wp-block-video\"><video controls src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/A.2-Prime-factorisation.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 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<h3 class=\"wp-block-heading has-text-color has-link-color has-normal-font-size wp-elements-07e5fb1ed3d22724f190434207a578c5\" style=\"color:#000060\"><strong>Key Concepts<\/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><strong><strong>Prime Numbers:<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><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>Composite Numbers:<\/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<ol class=\"wp-block-list has-large-font-size\">\n<li><\/li>\n<\/ol>\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>What<strong>How to Find Prime Factorisation<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><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><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><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><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><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<ol class=\"wp-block-list has-large-font-size\">\n<li><\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-normal-font-size wp-elements-d3361459707af7d015efa51891c6e21b\" style=\"color:#000060\"><strong>Example:<\/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><strong>Find the Prime Factorisation of 36<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\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-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\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>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 prime factorisation of 30.<\/li>\n\n\n\n<li>Find the prime factorisation of 56.<\/li>\n\n\n\n<li>Write 45 as a product of prime factors.<\/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>Why Prime Factorisation is Useful<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Simplifying Fractions:<\/strong><\/p>\n\n\n\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\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-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-dd3e0c36863a87b9ecd76a7c94f46e3c\" style=\"background-color:#f3c0c0\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><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-dc822d7ad4fedec4596376a16f4e79d2\" style=\"color:#b00012\"><strong>\u25b6\ufe0f Write the prime factorisation of 12. Use exponents when appropriate and order the factors from least to greatest (for example, 2<sup>2<\/sup> . 3 . 5 ).<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Divide by prime factors until the quotient is 1.<\/p>\n\n\n\n<p>12\u00f72 = 6<br>6\u00f72 = 3<br>3\u00f73 = 1<\/p>\n\n\n\n<p>The prime factorisation of 12 is:<\/p>\n\n\n\n<p>2 . 2 . 3<\/p>\n\n\n\n<p>Rewrite the repeated factor (2) with exponent.<\/p>\n\n\n\n<p>2<sup>2<\/sup> . 3<\/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-a60c0a9cfe77bf575280465da39387cc\" style=\"background-color:#e0d9fc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><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-8e0c18710744e4232e0e83820d472273\" style=\"color:#b00012\"><strong>\u25b6\ufe0f Write the prime factorisation of 20. Use exponents when appropriate and order the factors from least to greatest (for example, 2<sup>2<\/sup> . 3 . 5 ).<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Divide by prime factors until the quotient is 1.<\/p>\n\n\n\n<p>20\u00f72 = 10<br>10\u00f72 = 5<br>5\u00f75 = 1<\/p>\n\n\n\n<p>The prime factorisation of 20 is:<\/p>\n\n\n\n<p>2 . 2 . 5<\/p>\n\n\n\n<p>Rewrite the repeated factor (2) with exponent.<\/p>\n\n\n\n<p>2<sup>2<\/sup> . 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-39cd6adf8ffaa4ff37594b10eaf8fe9d\" style=\"background-color:#c9d6f9\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><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-fbb9bf05b1feae5ef538f3106246b8a8\" style=\"color:#b00012\">\u25b6\ufe0f <strong>Write the prime factorisation of 15. Use exponents when appropriate and order the factors from least to greatest (for example, 2<sup>2<\/sup> . 3 . 5 ).<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Divide by prime factors until the quotient is 1.<\/p>\n\n\n\n<p>15\u00f73 = 5<br>5\u00f75 = 1<\/p>\n\n\n\n<p>The prime factorisation of&nbsp;15&nbsp;is:<\/p>\n\n\n\n<p>3 . 5<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-normal-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\/95410\/302\/317\"><img decoding=\"async\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-4.png\" alt=\"\" class=\"wp-image-8426\"\/><\/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\/77974\/915\/860\"><img decoding=\"async\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-4.png\" alt=\"\" class=\"wp-image-8427\"\/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Prime factorisation 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: WhatHow to Find Prime Factorisation Start with the Number: Divide by the Smallest Prime Number:<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/a-5-prime-factorisation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;A.5 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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-19","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":25,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":18194,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/19\/revisions\/18194"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}