{"id":16089,"date":"2025-06-10T22:43:27","date_gmt":"2025-06-10T22:43:27","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=16089"},"modified":"2025-06-10T22:43:28","modified_gmt":"2025-06-10T22:43:28","slug":"express-900-as-a-product-of-its-prime-factors-in-index-form","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/express-900-as-a-product-of-its-prime-factors-in-index-form\/","title":{"rendered":"Express 900 as a product of its prime factors in index form"},"content":{"rendered":"\n<p>Express 900 as a product of its prime factors in index form. Write the prime factors in ascending order.<\/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\">Correct Answer:<\/h3>\n\n\n\n<p><strong>900 = 2\u00b2 \u00d7 3\u00b2 \u00d7 5\u00b2<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p>To express <strong>900<\/strong> as a product of its prime factors in <strong>index form<\/strong> (also known as exponential form), we must first understand what <strong>prime factorization<\/strong> means.<\/p>\n\n\n\n<p>A <strong>prime factor<\/strong> is a factor of a number that is a <strong>prime number<\/strong>\u2014a number greater than 1 that has no divisors other than 1 and itself. Examples of prime numbers include <strong>2, 3, 5, 7, 11<\/strong>, etc.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Step-by-step Prime Factorization of 900:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Start by dividing 900 by the smallest prime number (2):<\/strong><br>900 \u00f7 2 = 450<br>450 \u00f7 2 = 225<br>Since 225 is not divisible by 2, we move to the next prime. \u2705 Prime factor <strong>2<\/strong> appears <strong>2 times<\/strong> \u2192 2\u00b2<\/li>\n\n\n\n<li><strong>Next prime number is 3:<\/strong><br>225 \u00f7 3 = 75<br>75 \u00f7 3 = 25<br>25 is not divisible by 3, so we move on. \u2705 Prime factor <strong>3<\/strong> appears <strong>2 times<\/strong> \u2192 3\u00b2<\/li>\n\n\n\n<li><strong>Next prime number is 5:<\/strong><br>25 \u00f7 5 = 5<br>5 \u00f7 5 = 1 \u2705 Prime factor <strong>5<\/strong> appears <strong>2 times<\/strong> \u2192 5\u00b2<\/li>\n<\/ol>\n\n\n\n<p>Now, the division stops when we reach 1. We have fully broken down 900 into its <strong>prime components<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Step \u2013 Writing in Index Form:<\/h3>\n\n\n\n<p>Now write the prime factors in <strong>ascending order<\/strong> using indices (exponents):<\/p>\n\n\n\n<p><strong>900 = 2\u00b2 \u00d7 3\u00b2 \u00d7 5\u00b2<\/strong><\/p>\n\n\n\n<p>This is the <strong>prime factorization<\/strong> of 900 in <strong>index form<\/strong>, with all the prime numbers listed in increasing order (2, 3, and 5). This representation is compact, mathematically precise, and shows clearly how many times each prime number appears in the factorization of 900.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>This process helps in many mathematical applications, including simplifying fractions, finding greatest common divisors (GCD), least common multiples (LCM), and more.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Express 900 as a product of its prime factors in index form. Write the prime factors in ascending order. The correct answer and explanation is: Correct Answer: 900 = 2\u00b2 \u00d7 3\u00b2 \u00d7 5\u00b2 Explanation (300 words): To express 900 as a product of its prime factors in index form (also known as exponential form), [&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-16089","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16089","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=16089"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16089\/revisions"}],"predecessor-version":[{"id":16090,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16089\/revisions\/16090"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16089"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16089"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16089"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}