{"id":30374,"date":"2025-06-21T18:02:51","date_gmt":"2025-06-21T18:02:51","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=30374"},"modified":"2025-06-21T18:02:52","modified_gmt":"2025-06-21T18:02:52","slug":"what-is-the-prime-factorization-of-160-in-exponent-form","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-is-the-prime-factorization-of-160-in-exponent-form\/","title":{"rendered":"What is the prime factorization of 160 in exponent form"},"content":{"rendered":"\n<p>What is the prime factorization of 160 in exponent form?<\/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>The prime factorization of 160 in exponent form is:<\/p>\n\n\n\n<p><strong>160 = 2^5 \u00d7 5^1<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>To find the prime factorization of a number means to express it as a product of prime numbers raised to their respective powers.<\/p>\n\n\n\n<p>Start with 160 and divide it by the smallest prime number possible, which is 2:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>160 \u00f7 2 = 80<\/li>\n\n\n\n<li>80 \u00f7 2 = 40<\/li>\n\n\n\n<li>40 \u00f7 2 = 20<\/li>\n\n\n\n<li>20 \u00f7 2 = 10<\/li>\n\n\n\n<li>10 \u00f7 2 = 5<\/li>\n<\/ul>\n\n\n\n<p>At this point, 5 is no longer divisible by 2, so move to the next smallest prime number, which is 3. Since 5 is not divisible by 3, move to the next prime number, which is 5 itself:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 \u00f7 5 = 1<\/li>\n<\/ul>\n\n\n\n<p>Now, since the division resulted in 1, the factorization process is complete.<\/p>\n\n\n\n<p>Count how many times 2 was used as a factor. It was used 5 times (2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2). The prime 5 was used once.<\/p>\n\n\n\n<p>Thus, the prime factors are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2 raised to the power of 5, written as 2^5<\/li>\n\n\n\n<li>5 raised to the power of 1, written as 5^1<\/li>\n<\/ul>\n\n\n\n<p>Multiplying these prime factors confirms the original number:<\/p>\n\n\n\n<p>2^5 \u00d7 5^1 = 32 \u00d7 5 = 160<\/p>\n\n\n\n<p>This method ensures the number is broken down into its simplest building blocks\u2014prime numbers. Expressing the factorization in exponent form is a concise way to represent repeated multiplication of the same prime number.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is the prime factorization of 160 in exponent form? The correct answer and explanation is: The prime factorization of 160 in exponent form is: 160 = 2^5 \u00d7 5^1 Explanation: To find the prime factorization of a number means to express it as a product of prime numbers raised to their respective powers. Start [&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-30374","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30374","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=30374"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30374\/revisions"}],"predecessor-version":[{"id":30379,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/30374\/revisions\/30379"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=30374"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=30374"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=30374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}