{"id":32553,"date":"2017-08-21T18:48:17","date_gmt":"2017-08-21T18:48:17","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=32553"},"modified":"2026-03-25T11:39:39","modified_gmt":"2026-03-25T16:39:39","slug":"prime-factorization","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/prime-factorization\/","title":{"rendered":"Prime Factorization"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_Jl9w6g42Qfs\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_Jl9w6g42Qfs\" data-source-videoID=\"Jl9w6g42Qfs\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Prime Factorization Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Prime Factorization\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_Jl9w6g42Qfs:hover {cursor:pointer;} img#videoThumbnailImage_Jl9w6g42Qfs {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/07\/updated-prime-factorization-64a8529e2da86.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_Jl9w6g42Qfs\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_Jl9w6g42Qfs\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Prime Factorization\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_Jl9w6g42Qfs\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_Jl9w6g42Qfs\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_Jl9w6g42Qfs\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction gCL_Function() {\n  var x = document.getElementById(\"gCL\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"gCL_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"gCL\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#What_is_a_Prime_Number\" class=\"smooth-scroll\">What is a Prime Number?<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Identifying_Prime_Numbers\" class=\"smooth-scroll\">Identifying Prime Numbers<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Prime_Factorization\" class=\"smooth-scroll\">Prime Factorization<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Prime_Factorization_Practice_Questions\" class=\"smooth-scroll\">Prime Factorization Practice Questions<\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hey, guys! Welcome to this video on prime numbers and prime factorization.<\/p>\n<h2><span id=\"What_is_a_Prime_Number\" class=\"m-toc-anchor\"><\/span>What is a Prime Number?<\/h2>\n<p>\nA prime number is any number that can only be divided by either one or by itself.<\/p>\n<p>This means that a prime number will always be odd, except for the number 2. The only reason that is the case is because two is only the second numerical whole number. So, the only options for it to be divided by (without getting a fraction) are 1 and 2. Numerically, the first several prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. There are an infinite amount of prime numbers.<\/p>\n<h2><span id=\"Identifying_Prime_Numbers\" class=\"m-toc-anchor\"><\/span>Identifying Prime Numbers<\/h2>\n<p>\nLet\u2019s practice identifying prime numbers.<\/p>\n<p>Is 9 a prime number? Well, it can be divided by 1 and by itself, but are there any other numbers it can be divided by? Yes. 3 goes into 9 three times.<\/p>\n<p>What about 31? Is it a prime number? Yes. There is not another number other than 1 and itself that it can be divided by without getting a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/fractions\/\">fraction<\/a>!<\/p>\n<h2><span id=\"Prime_Factorization\" class=\"m-toc-anchor\"><\/span>Prime Factorization<\/h2>\n<p>\nNow, let\u2019s take a look at prime factorization.<\/p>\n<p>If you recall, <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/factors\/\">factors<\/a> are any numbers that you multiply together to get another number.<\/p>\n<p>Well, prime factorization uses this same concept, except you are only looking for the prime numbers that you are multiplying together to get the original number.<\/p>\n<h3><span id=\"Example_1\" class=\"m-toc-anchor\"><\/span>Example #1<\/h3>\n<p>\nWhat are the prime factors of 24?<\/p>\n<p>The easiest way to start is by starting with the smallest prime numbers, which will always be 2, so let\u2019s see if that works. <\/p>\n<p>So, 2 divides evenly into 24 to get 12, but 12 is not a prime number, so we must go even further.<\/p>\n<p>Let\u2019s try 3.<\/p>\n<p>3 worked as well, but our result still isn\u2019t a prime number. When we divide 3 into 12 we get 4, so we must go even further.<\/p>\n<p>Let\u2019s try 2 again.<\/p>\n<p>Great, so it worked! We\u2019ve gone the furthest we can go.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/prime-factoring-24@72.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>So, once we&#8217;ve factored everything out, to write this out to show our prime factorization, we&#8217;re only concerned with our prime numbers here.<\/p>\n<p>So what we have is \\(24=2\\times 3\\times 2\\times 2\\). We can even write this as \\(24=2^{3}\\times 3\\).<\/p>\n<h3><span id=\"Example_2\" class=\"m-toc-anchor\"><\/span>Example #2<\/h3>\n<p>\nLet\u2019s take a look at another one.<\/p>\n<p>What is the prime factorization of 72?<\/p>\n<p>Let\u2019s start with 2.<\/p>\n<p>2 goes into 72, 36 times; but 36 is not a prime number. So, we must go further.<\/p>\n<p>Let\u2019s try 3 now. 3 goes into 36, 12 times; but 12 is not a prime number.<\/p>\n<p>Let\u2019s try 3 again. 3 goes into 12, 4 times; but, yet again, 4 is not a prime number. So, We need to go further.<\/p>\n<p>2 goes into 4, 2 times.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/02\/prime-factoring-72@72.webp\" alt=\"\" width=\"\" height=\"\" class=\"aligncenter size-full wp-image-215971\"  role=\"img\" \/><\/p>\n<p>So now, we have our answer: \\(72=2^{3}\\times 3^{2}\\).<\/p>\n<p>Spend some time practicing prime factorization on your own. Remember, when you write out your answer, you are only concerned about the prime numbers that multiply together to get the original number.<\/p>\n<p>I hope this video has been helpful. For further help be sure to check out more of our videos by subscribing to our channel below.<\/p>\n<p>See you next time!<\/p>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Prime_Factorization_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Prime Factorization Practice Questions<\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the prime factorization of 100? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">\\(50\\times2\\)<\/div><div class=\"PQ\"  id=\"PQ-1-2\">\\(25\\times2^2\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-3\">\\(5^2\\times2^2\\)<\/div><div class=\"PQ\"  id=\"PQ-1-4\">\\(2^5\\times2^2\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The prime factorization is when we write a number in terms of their prime factors. For 100 we will start by multiplying 100 by 2, which gives us 50, then we keep breaking each number down:<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\(50\u00d72\\)<br \/>\n\\(25\u00d72\u00d72\\)<br \/>\n\\(5\u00d75\u00d72\u00d72\\)<br \/>\n\\(5^2\u00d72^2\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nThe prime factorization of which number is \\(2^4\u00d73^2\\)?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">36<\/div><div class=\"PQ\"  id=\"PQ-2-2\">48<\/div><div class=\"PQ\"  id=\"PQ-2-3\">96<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">144<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>When expanding an expression with exponents, you multiply the base by itself the number of times indicated by the exponent. This means \\(2^4\\) is saying we should multiply 2 by itself 4 times, or \\(2\u00d72\u00d72\u00d72\\), which is 16.<\/p>\n<p>Using the same definition, \\(3^2\\) is \\(3\u00d73\\), which is 9, and \\(16\u00d79\\) is 144.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the prime factorization of 1,323? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">\\(441\\times3\\)<\/div><div class=\"PQ\"  id=\"PQ-3-2\">\\(147\\times3^2\\)<\/div><div class=\"PQ\"  id=\"PQ-3-3\">\\(49\\times3^3\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-4\">\\(7^2\\times3^3\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>When writing a number by its prime factorization we must find all the prime factors. Generally, we start by dividing by either 2 or 3. It is obvious in this case that 2 cannot be a factor, so we start by dividing 1,323 by 3, which is 441.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\(441\u00d73\\)<br \/>\n\\(147\u00d73\u00d73\\)<br \/>\n\\(49\u00d73\u00d73\u00d73\\)<br \/>\n\\(7\u00d77\u00d73\u00d73\u00d73\\)<br \/>\n\\(7^2\u00d73^3\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich shows 1,125 as a prime factorization? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">\\(5^3\\times3^2\\)<\/div><div class=\"PQ\"  id=\"PQ-4-2\">\\(5^2\\times3^3\\)<\/div><div class=\"PQ\"  id=\"PQ-4-3\">\\(2^5\\times2^3\\)<\/div><div class=\"PQ\"  id=\"PQ-4-4\">\\(2^3\\times3^3\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>When we see a number that ends with 5, we know it is divisible by 5, so in this situation we will start to find the prime factors of 1,125 by first dividing it by 5, which is 225.<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\(225\u00d75\\)<br \/>\n\\(45\u00d75\u00d75\\)<br \/>\n\\(9\u00d75\u00d75\u00d75\\)<br \/>\n\\(3\u00d73\u00d75\u00d75\u00d75\\)<br \/>\n\\(5^3\u00d73^2\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhich shows 968 as a prime factorization?<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">\\(11\\times2^3\\)<\/div><div class=\"PQ\"  id=\"PQ-5-2\">\\(11^2\\times2^4\\)<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-3\">\\(11^2\\times2^3\\)<\/div><div class=\"PQ\"  id=\"PQ-5-4\">\\(121\\times2^3\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>Since 968 ends in 8, we will start by dividing it by 2, which is 484. Since 484 also ends in a factor of 2, we will divide by 2 again and get 242:<\/p>\n<p style=\"text-align:center; line-height: 35px\">\n\\(484\\times2\\)<br \/>\n\\(242\u00d72\u00d72\\)<br \/>\n\\(121\u00d72\u00d72\u00d72\\)<br \/>\n\\(11\u00d711\u00d72\u00d72\u00d72\\)<br \/>\n\\(11^2\u00d72^3\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/algebra-ii\/\">Return to Algebra II Videos<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Return to Algebra II Videos<\/p>\n","protected":false},"author":1,"featured_media":183176,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-32553","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-factoring-videos","7":"page_category-math-advertising-group","8":"page_category-video-pages-for-study-course-sidebar-ad","9":"page_type-video","10":"content_type-practice-questions","11":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/32553","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=32553"}],"version-history":[{"count":6,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/32553\/revisions"}],"predecessor-version":[{"id":263497,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/32553\/revisions\/263497"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/183176"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=32553"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}