{"id":36409,"date":"2025-06-25T07:14:37","date_gmt":"2025-06-25T07:14:37","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=36409"},"modified":"2025-06-25T07:14:39","modified_gmt":"2025-06-25T07:14:39","slug":"each-of-these-numbers-is-written-as-a-product-of-prime-factors","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/each-of-these-numbers-is-written-as-a-product-of-prime-factors\/","title":{"rendered":"Each of these numbers is written as a product of prime factors."},"content":{"rendered":"\n

Each of these numbers is written as a product of prime factors. 539 = 11 \\times 7^2 847 = 7 \\times 11^2 Use this information to write \\frac{539}{847} as a fraction in its simplest form,<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To simplify the fraction 539847\\frac{539}{847}, we begin by expressing each number using its prime factorization:<\/p>\n\n\n\n

539=11\u00d772,847=7\u00d7112539 = 11 \\times 7^2,\\quad 847 = 7 \\times 11^2<\/p>\n\n\n\n

Now write the fraction using these factorizations:<\/p>\n\n\n\n

539847=11\u00d7727\u00d7112\\frac{539}{847} = \\frac{11 \\times 7^2}{7 \\times 11^2}<\/p>\n\n\n\n

Next, cancel the common prime factors in the numerator and denominator. Both terms include the primes 7 and 11. The numerator has one factor of 11 and two of 7, while the denominator has two 11s and one 7:<\/p>\n\n\n\n

11\u00d77\u00d777\u00d711\u00d711\\frac{11 \\times 7 \\times 7}{7 \\times 11 \\times 11}<\/p>\n\n\n\n

Cancel one 7 and one 11 from top and bottom:<\/p>\n\n\n\n

711\\frac{7}{11}<\/p>\n\n\n\n

So the fraction in its simplest form is 711\\boxed{\\frac{7}{11}}.<\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

Simplifying a fraction involves reducing it by canceling out any common factors between the numerator and the denominator. The most effective method begins with expressing each number as a product of prime numbers. This is known as prime factorization.<\/p>\n\n\n\n

In this case, the numerator 539 breaks down into 11 multiplied by 7 twice, written as 11\u00d77211 \\times 7^2. The denominator 847 breaks down into 7 multiplied by 11 twice, or 7\u00d71127 \\times 11^2.<\/p>\n\n\n\n

Once these expressions are substituted into the original fraction, we are able to see shared components. Both contain at least one 7 and one 11. By canceling a matching pair of each from the top and bottom, we eliminate redundancy. What remains after cancellation is a single 7 in the numerator and a single 11 in the denominator.<\/p>\n\n\n\n

The result, 711\\frac{7}{11}, is now in its lowest terms because 7 and 11 are both prime and share no common divisors other than 1. This demonstrates the power of prime factorization as a tool for simplifying fractions logically and systematically.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Each of these numbers is written as a product of prime factors. 539 = 11 \\times 7^2 847 = 7 \\times 11^2 Use this information to write \\frac{539}{847} as a fraction in its simplest form, The Correct Answer and Explanation is: To simplify the fraction 539847\\frac{539}{847}, we begin by expressing each number using its prime […]<\/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-36409","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36409","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=36409"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36409\/revisions"}],"predecessor-version":[{"id":36420,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36409\/revisions\/36420"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=36409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=36409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=36409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}