{"id":35482,"date":"2025-06-24T11:13:19","date_gmt":"2025-06-24T11:13:19","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=35482"},"modified":"2025-06-24T11:13:20","modified_gmt":"2025-06-24T11:13:20","slug":"find-the-prime-factorisation-of-the-following-numbers","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-prime-factorisation-of-the-following-numbers\/","title":{"rendered":"Find the prime factorisation of the following numbers"},"content":{"rendered":"\n<p>Find the prime factorisation of the following numbers: (1) 72 (ii) 172 (iii) 450 (0) 8712 (vi) 13500 (iv) 980<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>Here is the prime factorisation of the given numbers:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>72<\/strong> = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 = 2\u00b3 \u00d7 3\u00b2<\/li>\n\n\n\n<li><strong>172<\/strong> = 2 \u00d7 2 \u00d7 43 = 2\u00b2 \u00d7 43<\/li>\n\n\n\n<li><strong>450<\/strong> = 2 \u00d7 3 \u00d7 3 \u00d7 5 \u00d7 5 = 2 \u00d7 3\u00b2 \u00d7 5\u00b2<\/li>\n\n\n\n<li><strong>8712<\/strong> = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 11 \u00d7 33 = 2\u00b3 \u00d7 3 \u00d7 11 \u00d7 33<\/li>\n\n\n\n<li><strong>980<\/strong> = 2 \u00d7 2 \u00d7 5 \u00d7 7 \u00d7 7 = 2\u00b2 \u00d7 5 \u00d7 7\u00b2<\/li>\n\n\n\n<li><strong>13500<\/strong> = 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 5 \u00d7 5 \u00d7 5 = 2\u00b2 \u00d7 3\u00b3 \u00d7 5\u00b3<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>Prime factorisation is the process of breaking down a composite number into a product of prime numbers. Prime numbers are numbers greater than 1 that have only two positive divisors \u2014 1 and the number itself. Examples of prime numbers include 2, 3, 5, 7, 11, and 13.<\/p>\n\n\n\n<p>To factorise a number into primes, we begin by dividing the number by the smallest prime, which is 2, and continue dividing until it is no longer divisible by that prime. We then move to the next smallest prime and repeat the process. This continues until we are left with 1.<\/p>\n\n\n\n<p>Let\u2019s take <strong>72<\/strong> as an example. Dividing by 2, we get:<br>72 \u00f7 2 = 36<br>36 \u00f7 2 = 18<br>18 \u00f7 2 = 9<br>9 is not divisible by 2, so we move to 3:<br>9 \u00f7 3 = 3<br>3 \u00f7 3 = 1<br>This gives the prime factorisation 2\u00b3 \u00d7 3\u00b2.<\/p>\n\n\n\n<p>For <strong>450<\/strong>, we divide:<br>450 \u00f7 2 = 225<br>225 \u00f7 3 = 75<br>75 \u00f7 3 = 25<br>25 \u00f7 5 = 5<br>5 \u00f7 5 = 1<br>So the prime factorisation is 2 \u00d7 3\u00b2 \u00d7 5\u00b2.<\/p>\n\n\n\n<p>This process helps identify the building blocks of a number and is useful in simplifying fractions, finding the greatest common divisor, least common multiple, and in various applications in algebra and number theory.<\/p>\n\n\n\n<p>Every whole number greater than 1 either is a prime or can be written uniquely as a product of prime numbers, which is known as the <strong>Fundamental Theorem of Arithmetic<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"722\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-313.jpeg\" alt=\"\" class=\"wp-image-35483\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-313.jpeg 722w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-313-212x300.jpeg 212w\" sizes=\"auto, (max-width: 722px) 100vw, 722px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Find the prime factorisation of the following numbers: (1) 72 (ii) 172 (iii) 450 (0) 8712 (vi) 13500 (iv) 980 The Correct Answer and Explanation is: Here is the prime factorisation of the given numbers: Explanation Prime factorisation is the process of breaking down a composite number into a product of prime numbers. Prime numbers [&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-35482","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35482","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=35482"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35482\/revisions"}],"predecessor-version":[{"id":35484,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35482\/revisions\/35484"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}