{"id":25419,"date":"2025-06-19T02:29:39","date_gmt":"2025-06-19T02:29:39","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25419"},"modified":"2025-06-19T02:29:41","modified_gmt":"2025-06-19T02:29:41","slug":"by-what-least-number-should-the-following-number-be-divided-to-get-a-perfect-square","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/by-what-least-number-should-the-following-number-be-divided-to-get-a-perfect-square\/","title":{"rendered":"By what least number should the following number be divided to get a perfect square."},"content":{"rendered":"\n<p>By what least number should the following number be divided to get a perfect square. a . 1275<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-green-cyan-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To determine the least number by which <strong>1275<\/strong> should be divided to obtain a <strong>perfect square<\/strong>, we begin by <strong>prime factorizing<\/strong> 1275.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Prime Factorization of 1275<\/h3>\n\n\n\n<p>Let\u2019s divide by the smallest prime numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1275 \u00f7 3 = 425<\/li>\n\n\n\n<li>425 \u00f7 5 = 85<\/li>\n\n\n\n<li>85 \u00f7 5 = 17<\/li>\n\n\n\n<li>17 is a prime number<\/li>\n<\/ul>\n\n\n\n<p>So,<br><strong>1275 = 3 \u00d7 5 \u00d7 5 \u00d7 17<\/strong><br>or<br><strong>1275 = 3 \u00d7 5\u00b2 \u00d7 17<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Understanding Perfect Squares<\/h3>\n\n\n\n<p>A perfect square has all prime factors in <strong>even powers<\/strong>.<br>From the factorization:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 appears once \u2192 <strong>odd<\/strong><\/li>\n\n\n\n<li>5 appears twice \u2192 <strong>even<\/strong><\/li>\n\n\n\n<li>17 appears once \u2192 <strong>odd<\/strong><\/li>\n<\/ul>\n\n\n\n<p>To make all the exponents even, we need to <strong>eliminate<\/strong> the primes that appear an <strong>odd<\/strong> number of times. So we must remove both 3 and 17 from the product.<\/p>\n\n\n\n<p>That means we should divide 1275 by <strong>3 \u00d7 17 = 51<\/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 Answer:<\/h3>\n\n\n\n<p>The <strong>least number<\/strong> by which 1275 should be divided to get a perfect square is <strong>51<\/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>To find the smallest number by which 1275 must be divided to produce a perfect square, we begin by factorizing it into its prime components. Prime factorization reveals the building blocks of a number and helps identify whether it can form a perfect square. A perfect square is a number whose prime factors all occur in even powers. For example, 36 = 2\u00b2 \u00d7 3\u00b2, which is a perfect square because each prime number is raised to an even power.<\/p>\n\n\n\n<p>Starting with 1275, we divide it by the smallest primes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1275 \u00f7 3 = 425<\/li>\n\n\n\n<li>425 \u00f7 5 = 85<\/li>\n\n\n\n<li>85 \u00f7 5 = 17<\/li>\n<\/ul>\n\n\n\n<p>This gives us the prime factorization: 1275 = 3 \u00d7 5\u00b2 \u00d7 17.<\/p>\n\n\n\n<p>Here, 3 and 17 are each raised to the power of one, which are odd powers. To make the number a perfect square, we must remove these two factors because they prevent the number from having only even exponents.<\/p>\n\n\n\n<p>Removing 3 and 17 means dividing the number by 3 \u00d7 17 = 51. After this division:<\/p>\n\n\n\n<p>1275 \u00f7 51 = 25<\/p>\n\n\n\n<p>Now 25 is a perfect square (since 25 = 5\u00b2), confirming our answer is correct. Therefore, dividing 1275 by 51 gives us the nearest perfect square with the smallest possible divisor.<\/p>\n\n\n\n<p>So, the least number by which 1275 must be divided to get a perfect square is <strong>51<\/strong>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-20.jpeg\" alt=\"\" class=\"wp-image-25420\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-20.jpeg 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-20-300x300.jpeg 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-20-150x150.jpeg 150w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-20-768x768.jpeg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>By what least number should the following number be divided to get a perfect square. a . 1275 The Correct Answer and Explanation is: To determine the least number by which 1275 should be divided to obtain a perfect square, we begin by prime factorizing 1275. Step 1: Prime Factorization of 1275 Let\u2019s divide by [&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-25419","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25419","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=25419"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25419\/revisions"}],"predecessor-version":[{"id":25421,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25419\/revisions\/25421"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}