{"id":236465,"date":"2025-06-16T09:14:33","date_gmt":"2025-06-16T09:14:33","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236465"},"modified":"2025-06-16T09:14:35","modified_gmt":"2025-06-16T09:14:35","slug":"write-168-as-the-product-of-prime-factors-index-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/write-168-as-the-product-of-prime-factors-index-form\/","title":{"rendered":"Write 168 as the product of prime factors (index form)"},"content":{"rendered":"\n

Write 168 as the product of prime factors (index form)<\/p>\n\n\n\n

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

Correct Answer:<\/strong><\/p>\n\n\n\n

168 = 2\u2073 \u00d7 3 \u00d7 7<\/p>\n\n\n\n

\n\n\n\n

Explanation<\/strong><\/p>\n\n\n\n

To express the number 168 as a product of its prime factors in index form, the process of prime factorization is used. This method involves breaking the number down into factors that are all prime numbers.<\/p>\n\n\n\n

The number 168 is even, meaning it is divisible by 2, the smallest prime number. Dividing 168 by 2 gives 84. Since 84 is also even, it can be divided by 2 again, giving 42. Continuing, 42 divided by 2 gives 21. At this point, 21 is no longer even and cannot be divided by 2 again.<\/p>\n\n\n\n

The next smallest prime number after 2 is 3. Dividing 21 by 3 gives 7. Finally, 7 is itself a prime number and cannot be broken down further.<\/p>\n\n\n\n

The complete prime factorization of 168 results in the prime numbers 2, 2, 2, 3, and 7. This can be written as a multiplication of these factors:
168 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 7.<\/p>\n\n\n\n

To write this in index form, similar prime numbers are grouped together and expressed using exponents. The number 2 appears three times, so it is expressed as 2\u00b3. The numbers 3 and 7 each appear once, so they are written as 3\u00b9 and 7\u00b9, although the exponent 1 is usually omitted in final form. Therefore, the product in index form is:
168 = 2\u00b3 \u00d7 3 \u00d7 7.<\/p>\n\n\n\n

Prime factorization plays an important role in various areas of mathematics, including simplifying fractions, finding greatest common factors, and solving problems involving divisibility. It reveals the building blocks of a number and provides insight into its structure, making it a valuable technique in both arithmetic and algebraic calculations.<\/p>\n\n\n\n

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

Write 168 as the product of prime factors (index form) The Correct Answer and Explanation is: Correct Answer: 168 = 2\u2073 \u00d7 3 \u00d7 7 Explanation To express the number 168 as a product of its prime factors in index form, the process of prime factorization is used. This method involves breaking the number down […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-236465","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236465","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=236465"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236465\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236465"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236465"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}