{"id":64,"date":"2022-04-08T04:30:22","date_gmt":"2022-04-08T04:30:22","guid":{"rendered":"http:\/\/6thclass.deltapublications.in\/?page_id=64"},"modified":"2025-09-10T06:11:49","modified_gmt":"2025-09-10T06:11:49","slug":"d-4-prime-factorisation-with-exponents","status":"publish","type":"page","link":"https:\/\/6thclass.deltapublications.in\/index.php\/d-4-prime-factorisation-with-exponents\/","title":{"rendered":"D.4 Prime factorisation with exponents"},"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 with exponents<\/strong><\/h2>\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<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<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>Prime Factorization:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\">Prime factorization is the process of breaking down a composite number into its prime factors, which are prime numbers that multiply together to give the original number.<\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Example:<\/strong> The prime factorization of 18 is 2\u00d73\u00d73, where 2 and 3 are prime numbers.<\/h2>\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>Exponents:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\">An exponent indicates how many times a number (called the base) is multiplied by itself.<\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Example:<\/strong> 3^2 (read as &#8220;three squared&#8221;) means 3\u00d73, which equals 9.<\/h2>\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>Using Exponents in Prime Factorization:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\">When a prime factor repeats in the prime factorization of a number, it can be expressed using an exponent.<\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Example:<\/strong> The prime factorization of 18 can be written as 2\u00d73^2, where the exponent 2 shows that 3 is used twice as a factor.<\/h2>\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>Steps to Find Prime Factorization with Exponents:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Step 1:<\/strong> Perform prime factorization by dividing the number by the smallest prime number.<\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Step 2:<\/strong> Continue dividing until you reach a quotient of 1.<\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Step 3:<\/strong> Write the prime factors, grouping identical prime numbers together.<\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Step 4:<\/strong> Use exponents to express repeated prime factors.<\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Example:<\/strong> The prime factorization of 72 is 2\u00d72\u00d72\u00d73\u00d73, which can 2^3 x 3^2<\/h2>\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>Why Use Exponents?<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\">Exponents simplify the expression of prime factorization, making it easier to read and understand.<\/h2>\n\n\n\n<h2 class=\"wp-block-heading has-normal-font-size\"><strong>Example:<\/strong> Instead of writing 2\u00d72\u00d72\u00d75 for 40, we can write 2^3\u00d75.<\/h2>\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><strong>Examples for Practice:<\/strong><\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Example 1: Prime Factorization of 36 with Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Step 1:<\/strong> Divide by 2: 36\u00f72=18<\/li>\n\n\n\n<li><strong>Step 2:<\/strong> Divide by 2: 18\u00f72=9<\/li>\n\n\n\n<li><strong>Step 3:<\/strong> Divide by 3: 9\u00f73=3<\/li>\n\n\n\n<li><strong>Step 4:<\/strong> Divide by 3: 3\u00f73=1<\/li>\n\n\n\n<li>Prime factorization: 2\u00d72\u00d73\u00d73=2^2 x 3^2<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Example 2: Prime Factorization of 48 with Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Step 1:<\/strong> Divide by 2: 48\u00f72=24<\/li>\n\n\n\n<li><strong>Step 2:<\/strong> Divide by 2: 24\u00f72=12<\/li>\n\n\n\n<li><strong>Step 3:<\/strong> Divide by 2: 12\u00f72=6<\/li>\n\n\n\n<li><strong>Step 4:<\/strong> Divide by 2: 6\u00f72=3<\/li>\n\n\n\n<li>3 is a prime number.<\/li>\n\n\n\n<li>Prime factorization: 2\u00d72\u00d72\u00d72\u00d73=2^4 x  3<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Example 3: Prime Factorization of 100 with Exponents<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Step 1:<\/strong> Divide by 2: 100\u00f72=50<\/li>\n\n\n\n<li><strong>Step 2:<\/strong> Divide by 2: 50\u00f72=25<\/li>\n\n\n\n<li><strong>Step 3:<\/strong> Divide by 5: 25\u00f75=5<\/li>\n\n\n\n<li><strong>Step 4:<\/strong> Divide by 5: 5\u00f75=1<\/li>\n\n\n\n<li>Prime factorization: 2\u00d72\u00d75\u00d75== 2^2 x 5^2<\/li>\n<\/ul>\n<\/div><\/div>\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-background has-normal-font-size\" style=\"background-color:#ecafaf\"><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-54ed142c2017abeeb93709c3ac7298b3\" style=\"color:#b00012\">\ud83d\udd14 Write the prime factorization of 4. Use exponents when appropriate and order the factors from least to greatest (for example, 2<sup>2<\/sup> . 3 . 5).<\/p>\n<\/div><\/div>\n\n\n\n<p>Divide&nbsp;by prime factors until the quotient is&nbsp;1.<\/p>\n\n\n\n<p>4\u00f72 = 2<br>2\u00f72 = 1<br>The prime factorization of 4 is:<br>2 . 2<\/p>\n\n\n\n<p>Rewrite&nbsp;the repeated factor&nbsp;(2)&nbsp;with&nbsp;exponent.<\/p>\n\n\n\n<p>2<sup>2<\/sup><\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#dcf2d0\"><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-a5b3a89714d673345807b20ad8f20a40\" style=\"color:#b00012\">\ud83d\udd14 Write the prime factorization of 8. Use exponents when appropriate and order the factors from least to greatest (for example, 2<sup>2 <\/sup>. 3 . 5 ).<\/p>\n<\/div><\/div>\n\n\n\n<p>Divide by prime factors until the quotient is 1.<br>8\u00f72 = 4<br>4\u00f72 = 2<br>2\u00f72 = 1<\/p>\n\n\n\n<p>The prime factorization of 8 is:<br>2 . 2 . 2<\/p>\n\n\n\n<p>Rewrite the repeated factor (2) with exponent.<br>2<sup>3<\/sup><\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b7dfee\"><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-a8575e5e6b44fcef249691aa53fa6d45\" style=\"color:#b00012\">Write the prime factorization of 8. Use exponents when appropriate and order the factors from least to greatest (for example, 2<sup>2<\/sup> . 3 . 5).<\/p>\n<\/div><\/div>\n\n\n\n<p>Divide by prime factors until the quotient is 1.<\/p>\n\n\n\n<p>8\u00f72 = 4<br>4\u00f72 = 2<br>2\u00f72 = 1<\/p>\n\n\n\n<p>The prime factorization of 8 is:<\/p>\n\n\n\n<p>2 . 2 . 2 <\/p>\n\n\n\n<p>Rewrite the repeated factor (2) with exponent.<\/p>\n\n\n\n<p>2<sup>3<\/sup><\/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\/76680\/129\/955\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-73.png\" alt=\"\" class=\"wp-image-6213\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-73.png 500w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-73-300x300.png 300w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-73-150x150.png 150w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-73-400x400.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\/97147\/355\/639\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74.png\" alt=\"\" class=\"wp-image-6214\" srcset=\"https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74.png 500w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74-300x300.png 300w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74-150x150.png 150w, https:\/\/6thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-74-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Prime factorization with exponents key notes: Prime Factorization: Prime factorization is the process of breaking down a composite number into its prime factors, which are prime numbers that multiply together to give the original number. Example: The prime factorization of 18 is 2\u00d73\u00d73, where 2 and 3 are prime numbers. Exponents: An exponent indicates how<a class=\"more-link\" href=\"https:\/\/6thclass.deltapublications.in\/index.php\/d-4-prime-factorisation-with-exponents\/\">Continue reading <span class=\"screen-reader-text\">&#8220;D.4 Prime factorisation with exponents&#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-64","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/64","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=64"}],"version-history":[{"count":37,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/64\/revisions"}],"predecessor-version":[{"id":16551,"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/64\/revisions\/16551"}],"wp:attachment":[{"href":"https:\/\/6thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=64"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}