{"id":62,"date":"2022-04-08T04:29:57","date_gmt":"2022-04-08T04:29:57","guid":{"rendered":"http:\/\/6thclass.deltapublications.in\/?page_id=62"},"modified":"2025-11-19T10:45:43","modified_gmt":"2025-11-19T10:45:43","slug":"d-3prime-factorisation","status":"publish","type":"page","link":"https:\/\/6thclass.deltapublications.in\/index.php\/d-3prime-factorisation\/","title":{"rendered":"D.3\tPrime factorisation"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Prime factorization<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/08\/A.2-Prime-factorisation.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-26e77fc4ba59d1d3deab8425210f245b\" style=\"color:#74008b;text-transform:capitalize\">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 Factorization?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors. As we know, a&nbsp;<a href=\"https:\/\/byjus.com\/maths\/composite-numbers\/\">composite number<\/a>&nbsp;has more than two factors, therefore, this method is applicable only for composite numbers and not for prime numbers.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">For example, the prime factors of 126 will be 2, 3 and 7 as 2 \u00d7 3&nbsp;\u00d7 3 \u00d7 7 = 126 and 2, 3, 7 are prime numbers.<\/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>Prime factorization Examples<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Prime factorization of 12 is 2&nbsp;\u00d7 2&nbsp;\u00d7 3 = 2<sup>2<\/sup>&nbsp;\u00d7 3<\/li>\n\n\n\n<li>Prime factorization of 18 is 2&nbsp;\u00d7 3&nbsp;\u00d7 3 = 2&nbsp;\u00d7 3<sup>2<\/sup><\/li>\n\n\n\n<li>Prime factorization of 24 is 2&nbsp;\u00d7 2&nbsp;\u00d7 2&nbsp;\u00d7 3 = 2<sup>3<\/sup>&nbsp;\u00d7 3<\/li>\n\n\n\n<li>Prime factorization of 20 is 2&nbsp;\u00d7 2&nbsp;\u00d7 5 = 2<sup>2<\/sup>&nbsp;\u00d7 5<\/li>\n\n\n\n<li>Prime factorization of 36 is 2&nbsp;\u00d7 2&nbsp;\u00d7 3&nbsp;\u00d7 3 = 2\u00b2 \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><strong>Prime Factors of a Number<\/strong> :<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">Prime factors of a number are the set of prime numbers which when multiplied by together give the actual number. Also, we can say, the prime factors divide the number completely. It is similar to&nbsp;<a href=\"https:\/\/byjus.com\/maths\/factors-of-a-number\/\">factoring a number<\/a>&nbsp;and considering only the prime numbers among the factors. For example, the prime factors of 6 will be 2 and 3, the prime factors of 26 will be 13 and 2, etc.<\/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>Prime Factorization Methods<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">The most commonly used prime factorization methods are:<\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Division Method<\/li>\n\n\n\n<li>Factor Tree Method<\/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>Division Method<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">The steps to calculate the prime factors of a number is similar to the process of finding the factors of a large number.&nbsp;Follow the below steps to find the prime factors of a number using the division method:<\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Step 1: Divide the given number by the smallest prime number. In this case, the smallest prime number should divide the number exactly.<\/li>\n\n\n\n<li>Step 2: Again, divide the quotient by the smallest prime number.<\/li>\n\n\n\n<li>Step 3: Repeat the process, until the quotient becomes 1.<\/li>\n\n\n\n<li>Step 4: Finally, multiply all the prime factors<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-group has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong>Example of Division Method for Prime Factorization:<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">Below is a detailed step-by-step process of prime factorization by taking 460 as an example.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 1:&nbsp;<\/strong>Divide 460 by the least prime number i.e. 2.<\/li>\n<\/ul>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; So, 460 \u00f7 2 = 230<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 2:&nbsp;<\/strong>Again Divide 230 with the least prime number (which is again 2).<\/li>\n<\/ul>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Now, 160 \u00f7 2 = 115<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 3:&nbsp;<\/strong>Divide again with the least prime number which will be 5.<\/li>\n<\/ul>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; So, 115 \u00f7 5 = 23<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Step 4:&nbsp;<\/strong>As 23 is a prime number, divide it with itself to get 1.<\/li>\n<\/ul>\n\n\n\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Now, the prime factors of 460 will be 2<sup>2<\/sup>&nbsp;x 5 x 23<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong>Factor Tree Method<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">To find the prime factorization of the given number using factor tree method, follow the below steps:<\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li>Step 1: Consider the given number as the root of the tree<\/li>\n\n\n\n<li>Step 2: Write down the pair of factors as the branches of a tree<\/li>\n\n\n\n<li>Step 3: Again factorize the composite factors, and write down the factors pairs as the branches<\/li>\n\n\n\n<li>Step 4: Repeat the step, until to find the prime factors of all the composite factors<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\">In factor tree, the factors of a number are found and then those numbers are further factorized until we reach the closure. Suppose we have to find the factors of 60 and 282 using a factor tree. Then see the diagram given below to understand the concept.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"306\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-66-1024x306.png\" alt=\"\" class=\"wp-image-13134\" style=\"width:753px;height:auto\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-66-1024x306.png 1024w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-66-300x90.png 300w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-66-768x229.png 768w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-66-1536x458.png 1536w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-66-2048x611.png 2048w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Untitled-design-66-1568x468.png 1568w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<p class=\"has-normal-font-size\">In the above figure, we can number 60 is first factorized into two numbers i.e. 6 and 10. Again, 6 and 10 is factorized to get the prime factors of 6 and 10, such that;<\/p>\n\n\n\n<p class=\"has-normal-font-size\">6 = 2 x 3<\/p>\n\n\n\n<p class=\"has-normal-font-size\">and 10 = 2 x 5<\/p>\n\n\n\n<p class=\"has-normal-font-size\">If we write the prime factors of 60 altogether, then;<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Prime factorization of 60 = 6 x 10 = 2 x 3 x 2 x 5<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Same is the case for number 282, such as;<\/p>\n\n\n\n<p class=\"has-normal-font-size\">282 = 2 x 141 = 2 x 3 x 47<\/p>\n\n\n\n<p class=\"has-normal-font-size\">So in both cases, a tree structure is formed<\/p>\n\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong>Prime Factorization Solved Examples<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\">An example question is given below which will help to understand the process of calculating the prime factors of a number easily.<\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Q.1:&nbsp;Find the prime factors of 1240.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"515\" height=\"221\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-11.png\" alt=\"\" class=\"wp-image-13141\" style=\"width:651px;height:auto\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-11.png 515w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-11-300x129.png 300w\" sizes=\"auto, (max-width: 515px) 100vw, 515px\" \/><\/figure><\/div>\n\n\n<p class=\"has-normal-font-size\"><strong>\u2234 The Prime Factors of 1240 will be 2<sup>3<\/sup>&nbsp;\u00d7 5 \u00d7 31.<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Q.2: Find the prime factors of 544.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"517\" height=\"268\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-10.png\" alt=\"\" class=\"wp-image-13139\" style=\"width:667px;height:auto\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-10.png 517w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-10-300x156.png 300w\" sizes=\"auto, (max-width: 517px) 100vw, 517px\" \/><\/figure><\/div>\n\n\n<p class=\"has-normal-font-size\">Therefore, the prime factors of 544 are 2<strong><sup>5<\/sup>&nbsp;<\/strong>x 17.<br><a><\/a><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\">Learn with an example<\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#aef6be\"><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-86165f38be0b371b3a337d5d1ae4a004\" style=\"color:#b00012\">\ud83d\udd14 What is the prime factorization of 2?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 \u00d7 3<\/li>\n\n\n\n<li>3 \u00d7 3<\/li>\n\n\n\n<li>2<\/li>\n\n\n\n<li>2 \u00d7 2<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>2 is a prime number. The prime factorization of 2 is 2.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f6cef2\"><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-2b4bb37dc057b6865eeaecbf58bc1fb6\" style=\"color:#b00012\">\ud83d\udd14 What is the prime factorization of 3?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3<\/li>\n\n\n\n<li>2 \u00d7 2 \u00d7 2<\/li>\n\n\n\n<li>2 \u00d7 3<\/li>\n\n\n\n<li>3 \u00d7 3<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>3 is a prime number. The prime factorization of 3 is 3.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b4f7f5\"><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-f8fcd158a4d382a97dfdb67c77182e15\" style=\"color:#b00012\">\ud83d\udd14 What is the prime factorisation of 18?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 \u00d7 3 \u00d7 3 \u00d7 3<\/li>\n\n\n\n<li>2 \u00d7 2 \u00d7 3 \u00d7 3<\/li>\n\n\n\n<li>2 \u00d7 3 \u00d7 3<\/li>\n\n\n\n<li>2 \u00d7 9<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Divide by prime factors until the quotient is 1.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>18 \u00f7 2 = 9<\/li>\n\n\n\n<li class=\"has-normal-font-size\">9 \u00f7 3 = 3<\/li>\n\n\n\n<li>3 \u00f7 3 = 1<\/li>\n<\/ul>\n\n\n\n<p>The prime factorization of 18 is:<\/p>\n\n\n\n<p>18 = 2 \u00d7 3 \u00d7 3<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/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\/76291\/318\/634\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-74.png\" alt=\"\" class=\"wp-image-6216\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-74.png 500w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-74-300x300.png 300w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-74-150x150.png 150w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-74-400x400.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\/30646\/404\/817\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75.png\" alt=\"\" class=\"wp-image-6217\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75.png 500w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75-300x300.png 300w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75-150x150.png 150w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Prime factorization key notes: What is Prime Factorization? Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors. As we know, a&nbsp;composite number&nbsp;has more than two factors, therefore, this method is applicable only for composite numbers and not for<a class=\"more-link\" href=\"https:\/\/6thclass.deltapublications.in\/index.php\/d-3prime-factorisation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;D.3\tPrime 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,"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-62","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/62","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=62"}],"version-history":[{"count":44,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/62\/revisions"}],"predecessor-version":[{"id":17357,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/62\/revisions\/17357"}],"wp:attachment":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=62"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}