{"id":27221,"date":"2025-06-19T21:38:51","date_gmt":"2025-06-19T21:38:51","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27221"},"modified":"2025-06-19T21:38:52","modified_gmt":"2025-06-19T21:38:52","slug":"write-down-the-prime-factorisation-of-48-in-index-form-and-show-your-working-in-a-factor-tree","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-down-the-prime-factorisation-of-48-in-index-form-and-show-your-working-in-a-factor-tree\/","title":{"rendered":"Write down the prime factorisation of 48 in index form, and show your working in a factor tree"},"content":{"rendered":"\n<p>Write down the prime factorisation of 48 in index form, and show your working in a factor tree.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Prime Factorisation of 48 in Index Form<\/strong><\/h3>\n\n\n\n<p>The <strong>prime factorisation of 48<\/strong> is:<br><strong>48 = 2\u2074 \u00d7 3<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83c\udf32 <strong>Factor Tree of 48<\/strong><\/h3>\n\n\n\n<p>Here\u2019s how a factor tree would break down 48 into its prime factors:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>        48\n       \/  \\\n      6    8\n     \/ \\   \/ \\\n    2  3  2  4\n            \/ \\\n           2  2\n<\/code><\/pre>\n\n\n\n<p>Now gather all the prime numbers from the ends of the branches:<br><strong>2, 3, 2, 2, 2<\/strong><br>Group the 2s together:<br><strong>2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3 = 2\u2074 \u00d7 3<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 <strong>300-Word Explanation<\/strong><\/h3>\n\n\n\n<p><strong>Prime factorisation<\/strong> is the process of expressing a whole number as the product of its <strong>prime numbers<\/strong>\u2014numbers that can only be divided by 1 and themselves (like 2, 3, 5, 7, 11, etc.). In the case of <strong>48<\/strong>, the goal is to break it down until every factor is a prime number.<\/p>\n\n\n\n<p>To do this, we can use a <strong>factor tree<\/strong>, which is a visual method of finding all the prime factors of a number. We start by splitting 48 into two smaller factors. For example, 48 can be broken down into <strong>6 and 8<\/strong>. These are not prime numbers, so we break them down further:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>6 = 2 \u00d7 3 (both prime)<\/li>\n\n\n\n<li>8 = 2 \u00d7 4 (4 is not prime, so split again: 4 = 2 \u00d7 2)<\/li>\n<\/ul>\n\n\n\n<p>At the end, all branches lead to prime numbers: <strong>2, 2, 2, 2, and 3<\/strong>. We count how many times each prime number appears:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 appears <strong>four times<\/strong><\/li>\n\n\n\n<li>3 appears <strong>once<\/strong><\/li>\n<\/ul>\n\n\n\n<p>So, in <strong>index form<\/strong> (also called <strong>exponential form<\/strong>), the prime factorisation of 48 is written as:<br><strong>2\u2074 \u00d7 3<\/strong><\/p>\n\n\n\n<p>This method ensures the number is broken down into its simplest building blocks. Factor trees can vary in structure (e.g., starting with 4 \u00d7 12 or 2 \u00d7 24), but they will always lead to the <strong>same prime factors<\/strong>, proving that <strong>prime factorisation is unique for each number<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write down the prime factorisation of 48 in index form, and show your working in a factor tree. The correct answer and explanation is: \u2705 Prime Factorisation of 48 in Index Form The prime factorisation of 48 is:48 = 2\u2074 \u00d7 3 \ud83c\udf32 Factor Tree of 48 Here\u2019s how a factor tree would break down [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-27221","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27221","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=27221"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27221\/revisions"}],"predecessor-version":[{"id":27224,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27221\/revisions\/27224"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27221"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}