{"id":26514,"date":"2025-06-19T15:50:25","date_gmt":"2025-06-19T15:50:25","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26514"},"modified":"2025-06-19T15:50:27","modified_gmt":"2025-06-19T15:50:27","slug":"write-the-number-45-as-a-product-of-prime-factor-45","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/write-the-number-45-as-a-product-of-prime-factor-45\/","title":{"rendered":"Write the number 45 as a product of prime factor 45"},"content":{"rendered":"\n<p>Write the number 45 as a product of prime factor 45<\/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<p><strong>Answer:<\/strong><br>The number 45 can be written as a product of prime factors as:<br><strong>45 = 3 \u00d7 3 \u00d7 5<\/strong> or <strong>45 = 3\u00b2 \u00d7 5<\/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:<\/h3>\n\n\n\n<p>Prime factorization is the process of expressing a composite number as a product of its prime numbers. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. Examples include 2, 3, 5, 7, 11, and so on.<\/p>\n\n\n\n<p>To find the prime factors of 45, follow these steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Start dividing by the smallest prime number, 2:<\/strong><br>Since 45 is odd, it\u2019s not divisible by 2.<\/li>\n\n\n\n<li><strong>Try the next prime number, 3:<\/strong><br>45 \u00f7 3 = 15<br>So, 3 is a prime factor.<\/li>\n\n\n\n<li><strong>Continue factoring 15:<\/strong><br>15 \u00f7 3 = 5<br>Here, 3 is again a factor, and 5 is the quotient.<\/li>\n\n\n\n<li><strong>Check if 5 is prime:<\/strong><br>Yes, 5 is a prime number.<\/li>\n<\/ol>\n\n\n\n<p>At this point, we have completely factored 45 into prime numbers: 3, 3, and 5.<\/p>\n\n\n\n<p>Therefore:<br><strong>45 = 3 \u00d7 3 \u00d7 5 = 3\u00b2 \u00d7 5<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Why is prime factorization important?<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Fundamental Theorem of Arithmetic:<\/strong> Every positive integer greater than 1 can be expressed uniquely as a product of prime numbers, except for the order of the factors. This theorem guarantees that the prime factorization is unique.<\/li>\n\n\n\n<li><strong>Simplifying fractions:<\/strong> Prime factors help in reducing fractions to their simplest form by canceling common factors.<\/li>\n\n\n\n<li><strong>Finding the Greatest Common Divisor (GCD) and Least Common Multiple (LCM):<\/strong> These are calculated easily using prime factorizations of the numbers involved.<\/li>\n\n\n\n<li><strong>Cryptography and Computer Science:<\/strong> Prime factorization plays a vital role in security algorithms, such as RSA encryption.<\/li>\n<\/ul>\n\n\n\n<p>By understanding the prime factors of a number like 45, we gain insight into its divisibility properties and can solve many mathematical problems more efficiently.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write the number 45 as a product of prime factor 45 The correct answer and explanation is: Answer:The number 45 can be written as a product of prime factors as:45 = 3 \u00d7 3 \u00d7 5 or 45 = 3\u00b2 \u00d7 5 Explanation: Prime factorization is the process of expressing a composite number as a [&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-26514","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26514","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=26514"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26514\/revisions"}],"predecessor-version":[{"id":26515,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26514\/revisions\/26515"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26514"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26514"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26514"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}