{"id":43333,"date":"2025-03-21T14:26:26","date_gmt":"2025-03-21T06:26:26","guid":{"rendered":"https:\/\/www.wukongsch.com\/blog\/?p=43333"},"modified":"2026-01-26T15:48:02","modified_gmt":"2026-01-26T07:48:02","slug":"factors-of-21","status":"publish","type":"post","link":"https:\/\/www.wukongsch.com\/blog\/factors-of-21-post-43333\/","title":{"rendered":"Factors of 21:A Easy Guide From Concept to Practice"},"content":{"rendered":"<div style=\"margin-top: 0px; margin-bottom: 0px;\" class=\"sharethis-inline-share-buttons\" ><\/div>\n<p>If you\u2019ve ever wondered what numbers can team up to create 21 through multiplication, you\u2019re in the right place.Factors are like building blocks of a number. For example, 3 and 7 are factors of 21 because when you multiply them (3 \u00d7 7), you get 21.<\/p>\n\n\n\n<p>In this article, <a href=\"https:\/\/www.wukongsch.com\/\">Wukong Education<\/a> will explore what all the factors of 21 are, how to find factors of 21 using simple methods like division and multiplication, and dive into concepts like prime factorization, factor trees, and factor in pairs. We\u2019ll also look at examples and discuss common mistakes to help you master the topic with confidence.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"1024\" height=\"1018\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-1024x1018.webp\" alt=\"the factors of 21\" class=\"wp-image-57031\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-1024x1018.webp 1024w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-300x298.webp 300w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-150x150.webp 150w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-768x764.webp 768w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-920x915.webp 920w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-200x200.webp 200w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-120x120.webp 120w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/364bf93e-7a12-43e8-b311-05f98f7cbfb9-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 1086w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"what-are-the-factors-of-21\"><\/span>What are the factors of 21?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Understanding the factors of 21 is essential in mathematics, as it helps in various mathematical operations such as <a href=\"https:\/\/www.wukongsch.com\/blog\/division-math-problems-post-41204\/\">division<\/a>, multiplication, and finding the greatest common factor (GCF) or least common multiple (LCM) of two numbers. The factors of 21 are the numbers that divide 21 exactly without leaving a remainder. These factors can be positive or negative integers.<\/p>\n<div class=\"retention-card-new\" data-lang=\"en\" data-subject=\"MATH\" data-btnName=\"Get started free!\" data-subTitle=\"Suitable for students worldwide, from grades 1 to 12.\">\r\n    <div class=\"retention-card-l\">\r\n        <div class=\"trustpilot-image\"><\/div>\r\n        <h3><p>Discovering the maths whiz in every child,<br \/>\n<span>that&#8217;s what we do.<\/span><\/p>\n<\/h3>\r\n        <p>Suitable for students worldwide, from grades 1 to 12.<\/p>\r\n        <a class=\"retention-card-button is-point\" href=\"https:\/\/www.wukongsch.com\/independent-appointment\/?subject=math&amp;l=eafd8b18-486b-4e0a-b93d-4105d41d2067&amp;booking_triggerevent=BLOG_DETAIL_MODEL_CTA_BUTTON\" data-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u70b9\u51fb\" data-event=\"C_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" data-expose-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u66dd\u5149\" data-expose-event=\"D_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" target=\"_blank\" title=\"Get started free!\">\r\n            Get started free!\r\n        <\/a>\r\n    <\/div>\r\n    <div class=\"retention-card-r\"><\/div>\r\n<\/div>\n\n\n<p>The smallest factor of 21 is 1. For the number 21, its factors are the numbers that can divide it evenly with zero remainder. Let\u2019s break it down:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 \u00d7 21 = 21, so 1 and 21 are factors of 21.<\/li>\n\n\n\n<li>3 \u00d7 7 = 21, so 3 and 7 are also factors of 21.<\/li>\n<\/ul>\n\n\n\n<p>These are the only numbers that work. Therefore, the factors of 21 are 1, 3, 7, and 21.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"485\" height=\"269\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/24191cf2-9a17-4270-9f8a-d1ebf08e2b32-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"factors of 21 from wukong\" class=\"wp-image-57032\" style=\"width:761px;height:auto\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/24191cf2-9a17-4270-9f8a-d1ebf08e2b32-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 485w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/24191cf2-9a17-4270-9f8a-d1ebf08e2b32-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-300x166.webp 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/figure><\/div>\n\n\n<p>Negative integers can also be factors if they multiply together to give 21. For example, -1, -3, -7, and -21 are negative factors of 21 because (-1) \u00d7 (-21) = 21 and (-3) \u00d7 (-7) = 21.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"891\" height=\"285\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/d7faca94-940c-4a3b-aa56-aaae62d73e05-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"positive factors of 21\" class=\"wp-image-57033\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/d7faca94-940c-4a3b-aa56-aaae62d73e05-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 891w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/d7faca94-940c-4a3b-aa56-aaae62d73e05-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-300x96.webp 300w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/d7faca94-940c-4a3b-aa56-aaae62d73e05-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-768x246.webp 768w\" sizes=\"(max-width: 891px) 100vw, 891px\" \/><\/figure>\n\n\n\n<p>Understanding both positive and negative factors is crucial, especially when solving equations or working with algebraic expressions. Knowing the factors of a number like 21 can simplify complex problems and make mathematical operations more manageable.Now, let\u2019s move on to how we can find these factors using different methods.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"how-to-find-the-factors-of-21\"><\/span>How to find the factors of 21?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>There are two simple ways to find the factors of 21: the <strong>multiplication method<\/strong> and the <strong>division method<\/strong>. Pair factors are pairs of numbers that multiply to give 21. Let\u2019s explore both.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Factors of 21 by Multiplication Method<\/h3>\n\n\n\n<p>In this method, we look for pairs of numbers that multiply together to give 21. Here\u2019s how it works:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Start with 1 \u00d7 21 = 21. This means 1 and 21 are factors.<\/li>\n\n\n\n<li>Next, try 3 \u00d7 7 = 21. This means 3 and 7 are also factors.<\/li>\n\n\n\n<li>Negative pair factors like (-3) and (-7) also multiply to give 21.<\/li>\n\n\n\n<li>There are no other whole numbers that multiply to give 21, so we stop here.<\/li>\n<\/ul>\n\n\n\n<p>Using this method, we find the factors of 21 are 1, 3, 7, and 21.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Factors of 21 by Division Method<\/h3>\n\n\n\n<p>In this method, we divide 21 by different numbers to see if they leave no remainder. Here\u2019s how it works:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Divide 21 by 1: 21 \u00f7 1 = 21. Since there\u2019s no remainder, 1 and 21 are factors.<\/li>\n\n\n\n<li>Divide 21 by 3: 21 \u00f7 3 = 7. Since there\u2019s no remainder, 3 and 7 are factors.<\/li>\n\n\n\n<li>Divide 21 by 7: 21 \u00f7 7 = 3. Again, no remainder, so 7 and 3 are factors.<\/li>\n\n\n\n<li>Divide 21 by 21: 21 \u00f7 21 = 1. No remainder, so 21 and 1 are factors.<\/li>\n<\/ul>\n\n\n\n<p>If we try dividing 21 by numbers like 2, 4, 5, or 6, they leave remainders, so they are not factors.<\/p>\n\n\n\n<p>Using both methods, we confirm that the factors of 21 are <strong>1, 3, 7, and 21<\/strong>.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prime-factorization-of-21\"><\/span>Prime Factorization of 21<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Prime factorization is a way of breaking down a number into its smallest building blocks\u2014<a href=\"https:\/\/www.wukongsch.com\/blog\/division-math-problems-post-41204\/\">prime numbers<\/a>. For example, the prime factors of 21 are 3 and 7. Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"258\" height=\"254\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/d1b87c19-6347-432a-9bc7-4d9fc31cdd57-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"Prime Factorization of 21\" class=\"wp-image-57034\" style=\"width:322px;height:auto\"\/><\/figure><\/div>\n\n\n<p>Let\u2019s explore it step by step:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Start with the smallest prime number, which is 2. Can 21 be divided by 2? No, because 21 is an odd number.<\/li>\n\n\n\n<li>Move to the next prime number, which is 3. Divide 21 by 3:<\/li>\n\n\n\n<li>21 \u00f7 3 = 7.<\/li>\n\n\n\n<li>Now, we have 3 and 7.<\/li>\n\n\n\n<li>Check if 7 is a prime number. Since 7 can only be divided by 1 and itself, it is a prime number.<\/li>\n<\/ol>\n\n\n\n<p>So, the prime factorization of 21 is <strong>3 \u00d7 7<\/strong>. These are the prime numbers that multiply together to give 21.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"factor-tree-of-21\"><\/span>Factor Tree of 21<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>The <strong>factor tree of 21<\/strong> is a visual way to break the number 21 into its <strong>prime factors<\/strong> step by step. A factor tree helps students clearly understand <strong>prime factorization<\/strong>, which is an important skill in many math topics, such as finding the <strong>greatest common factor (GCF)<\/strong> and <strong>simplifying fractions<\/strong>.<\/p>\n\n\n\n<p>Below are the steps to create a <strong>factor tree of 21<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Start with the Number<\/strong><\/h3>\n\n\n\n<p>Begin at the top of the factor tree with the number <strong>21<\/strong>.<br>This is the number we want to break down into smaller factors.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Divide by the Smallest Prime Number<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The smallest prime number is <strong>2<\/strong><\/li>\n\n\n\n<li>Check whether 21 can be divided evenly by 2:<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>21 \u00f7 2 = 10.5\n<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since the result is <strong>not a whole number<\/strong>, <strong>2 is not a factor of 21<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 Move on to the next smallest prime number.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Continue Factorization<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The next smallest prime number is <strong>3<\/strong><\/li>\n\n\n\n<li>Divide 21 by 3:<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>21 \u00f7 3 = 7\n<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The result is a whole number, so <strong>3 is a factor of 21<\/strong><\/li>\n<\/ul>\n\n\n\n<p>In the factor tree:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Write <strong>3<\/strong> as one branch connected to 21<\/li>\n\n\n\n<li>Write <strong>7<\/strong> on the next level as the remaining number<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 4: Factor the Next Number<\/strong><\/h3>\n\n\n\n<p>Now look at the number <strong>7<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7 can only be divided by <strong>1 and 7<\/strong><\/li>\n\n\n\n<li>This means <strong>7 is a prime number<\/strong><\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 Since 7 is prime, it cannot be factored any further.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 5: Identify the Prime Factors<\/strong><\/h3>\n\n\n\n<p>At this point, all the numbers at the ends of the factor tree are prime:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>3<\/strong><\/li>\n\n\n\n<li><strong>7<\/strong><\/li>\n<\/ul>\n\n\n\n<p>This means the factorization is complete.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 6: Complete the Factor Tree<\/strong><\/h3>\n\n\n\n<p>The completed <strong>factor tree of 21<\/strong> looks like this:<\/p>\n\n\n\n<p>\ud83d\udc49 <strong>3 \u00d7 7<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"306\" height=\"338\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/b52a82f5-a1d1-421f-824e-ba10128c6ef5-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"the Factor  of  21 Tree\" class=\"wp-image-57035\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/b52a82f5-a1d1-421f-824e-ba10128c6ef5-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 306w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/b52a82f5-a1d1-421f-824e-ba10128c6ef5-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-272x300.webp 272w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading\"><strong>Note: Prime Factorization of 21<\/strong><\/h3>\n\n\n\n<p>So, the <strong>prime factorization of 21<\/strong> is:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>21 = 3 \u00d7 7<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Quick Tip for Students<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A factor tree helps you break a number into <strong>prime numbers<\/strong><\/li>\n\n\n\n<li>Always try dividing by the <strong>smallest prime number first<\/strong><\/li>\n\n\n\n<li>Stop when all the branches end in prime numbers<\/li>\n\n\n\n<li>The factor tree of 21 is simple and perfect for beginners to practice<\/li>\n<\/ul>\n\n\n\n<p>A factor tree is a visual way to break down a number of its prime factors. It\u2019s like drawing a tree where the branches split into smaller and smaller factors until we reach the prime numbers.<\/p>\n\n\n\n<p>Let\u2019s build a factor tree for 21:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Start with the number <strong>21<\/strong> at the top of the tree.<\/li>\n\n\n\n<li>Think of two numbers that multiply to give 21. We know 3 \u00d7 7 = 21, so we draw two branches: one for <strong>3<\/strong> and one for <strong>7<\/strong>.<\/li>\n\n\n\n<li>Now, check if 3 and 7 can be broken down further.\n<ol class=\"wp-block-list\">\n<li>3 is a prime number (it can only be divided by 1 and itself), so we stop here.<\/li>\n\n\n\n<li>7 is also a prime number, so we stop here as well.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n\n<p>The factor tree for 21 looks like this:<\/p>\n\n\n\n<p>At the bottom of the tree, we have the prime factors of : <strong>3 and 7<\/strong>. This shows that 21 is made by multiplying these two numbers together.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"factor-pairs-of-21\"><\/span>Factor Pairs of 21<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Factor pairs are two numbers that multiply together to give the original number. For 21, we can find both positive factor pairs and negative factor pairs. Let\u2019s explore both:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Positive Factor Pairs of 21<\/strong><\/h3>\n\n\n\n<p>These are pairs of positive numbers that multiply to give 21. Using the factors we already know (1, 3, 7, 21), we can list a table:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Factor Pair<\/strong><\/td><td><strong>Multiplication<\/strong><\/td><\/tr><tr><td>1 \u00d7 21<\/td><td>1 \u00d7 21 = 21<\/td><\/tr><tr><td>3 \u00d7 7<\/td><td>3 \u00d7 7 = 21<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>These are the only positive pairs that work.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Negative Factor Pairs of 21<\/h3>\n\n\n\n<p>Negative factor pairs are pairs of negative numbers that multiply to give 21. Remember, multiplying two negative numbers gives a positive result. Here are the negative factor pairs:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Factor Pair<\/strong><\/td><td><strong>Multiplication<\/strong><\/td><\/tr><tr><td>(-1) \u00d7 (-21)<\/td><td>(-1) \u00d7 (-21) = 21<\/td><\/tr><tr><td>(-3) \u00d7 (-7)<\/td><td>(-3) \u00d7 (-7) = 21<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>These pairs also multiply to give 21, but they use negative numbers.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary of Factor Pairs<\/h3>\n\n\n\n<p>Here\u2019s a table summarizing all the factor pairs of 21:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>Positive Pairs<\/strong><\/td><td><strong>Negative Pairs<\/strong><\/td><\/tr><tr><td>1 \u00d7 21<\/td><td>(-1) \u00d7 (-21)<\/td><\/tr><tr><td>3 \u00d7 7<\/td><td>(-3) \u00d7 (-7)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Whether positive or negative, these pairs all multiply to give 21.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"solved-examples-on-factors-of-21\"><\/span>Solved Examples on Factors of 21<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>1.What Is the Greatest Common Factors of 21?<\/strong><\/p>\n\n\n\n<p>The <strong>Greatest Common Factor (GCF)<\/strong> of 21 depends on the other number you\u2019re comparing it to. For example:<\/p>\n\n\n\n<p>GCF of 21 and 28 is 7 (since 7 is the largest number that divides both 21 and 28).<\/p>\n\n\n\n<p>GCF of 21 and 63 is 21 (since 21 is the largest number that divides both 21 and 63).<\/p>\n\n\n\n<p>Hence, the GCF of 21 varies depending on the other number.<\/p>\n\n\n\n<p><strong>2.What are the common factors of 21 and 14? and How many common factors do 21 and 14 have?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"288\" height=\"234\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/d3f77e2a-4425-4251-81b2-12c03e99a7cb-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"2.What are the common factors of 21 and 14? and How many common factors do 21 and 14 have?\" class=\"wp-image-57036\"\/><\/figure><\/div>\n\n\n<p>List the factors of 21: 1, 3, 7, 21.<\/p>\n\n\n\n<p>List the factors of 14: 1, 2, 7, 14.<\/p>\n\n\n\n<p>Identify the common factors: 1 and 7.<\/p>\n\n\n\n<p>Hence, the common factors of 21 and 14 are 1 and 7. Besides, 21 and 14 have 2 common factors.<\/p>\n\n\n\n<p><strong>3. What is the Greast Common Factor of 21 and 14?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"340\" height=\"77\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/ea1707ea-4a90-4f7f-956a-24ab63175263-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"3. What is the Greast Common Factor of 21 and 14?\" class=\"wp-image-57037\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/ea1707ea-4a90-4f7f-956a-24ab63175263-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 340w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/ea1707ea-4a90-4f7f-956a-24ab63175263-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-300x68.webp 300w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><\/figure><\/div>\n\n\n<p>List the factors of 14: 1, 2, 7, 14.<\/p>\n\n\n\n<p>List the factors of 21: 1, 3, 7, 21.<\/p>\n\n\n\n<p>Identify the common factors: 1 and 7.<\/p>\n\n\n\n<p>The greatest common factor (GCF) is the largest common factor, which is 7.<\/p>\n\n\n\n<p>Hence, the GCF of 14 and 21 is 7.<\/p>\n\n\n\n<p><strong>4. A teacher has 21 students and wants to divide them into equal groups for a project. If each group must have the same number of students, how many students can be in each group? List all the possible ways.<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img decoding=\"async\" width=\"1024\" height=\"932\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/students-in-equal-groups-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-1024x932.webp\" alt=\"factors\" class=\"wp-image-57038\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/students-in-equal-groups-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-1024x932.webp 1024w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/students-in-equal-groups-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-300x273.webp 300w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/students-in-equal-groups-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-768x699.webp 768w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/students-in-equal-groups-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-920x838.webp 920w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/students-in-equal-groups-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 1186w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<p>Use the factors of 21: 1, 3, 7, 21.<\/p>\n\n\n\n<p>List possible group sizes:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>1 group of 21 students.<\/li>\n\n\n\n<li>3 groups of 7 students each.<\/li>\n\n\n\n<li>7 groups of 3 students each.<\/li>\n\n\n\n<li>21 groups of 1 student each.<\/li>\n<\/ol>\n\n\n\n<p>Hence, the students can be divided into groups of 1, 3, 7, or 21.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"common-mistakes-and-how-to-avoid-it\"><\/span>Common Mistakes and How to Avoid it<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1.<strong> Forgetting 1 and the Number Itself<\/strong><\/h3>\n\n\n\n<p>Example: A student lists the factors of 21 as 3 and 7, forgetting 1 and 21.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" width=\"382\" height=\"187\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/ea5c94f3-1770-43a0-9ef5-5bd8b7e28e8d-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"facor of 21 from wukong\" class=\"wp-image-57040\" style=\"width:630px;height:auto\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/ea5c94f3-1770-43a0-9ef5-5bd8b7e28e8d-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 382w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/ea5c94f3-1770-43a0-9ef5-5bd8b7e28e8d-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-300x147.webp 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/figure><\/div>\n\n\n<p>Why it\u2019s wrong: Every number has at least two factors: 1 and itself.<\/p>\n\n\n\n<p>How to avoid it: Always start by writing 1 and the number itself as factors. For 21, start with 1 and 21, then find the others.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>2. Missing Factors<\/strong><\/h3>\n\n\n\n<p>Example: A student thinks the factors of 21 are only 1, 7, and 21, missing 3.<\/p>\n\n\n\n<p>Why it\u2019s wrong: Factors come in pairs. If you find one factor, there\u2019s always another that pairs with it.<\/p>\n\n\n\n<p>How to avoid it: Use the multiplication or division method to check all possible pairs. For 21, test numbers like 3 (since 3 \u00d7 7 = 21).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3.<strong> Confusing Factors with Multiples<\/strong><\/h3>\n\n\n\n<p>Example: A student says 42 is a factor of 21 because 21 \u00d7 2 = 42.<\/p>\n\n\n\n<p>Why it\u2019s wrong: Factors are smaller than or equal to the number, while multiples are larger.<\/p>\n\n\n\n<p>How to avoid it: Remember that factors divide the number evenly, while multiples are the result of multiplying the number by another whole number.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4.<strong> Ignoring Negative Factors<\/strong><\/h3>\n\n\n\n<p>Example: A student lists only positive factors of 21, forgetting negative pairs like (-3) \u00d7 (-7) = 21.<\/p>\n\n\n\n<p>Why it\u2019s wrong: Factors can be negative if they multiply to give the original number.<\/p>\n\n\n\n<p>How to avoid it: When asked for all factors, include both positive and negative pairs.<\/p>\n\n\n\n<p>By being aware of these common mistakes and following the tips to avoid them, you\u2019ll become more confident and accurate when working with factors. Keep practicing, and you\u2019ll master this topic in no time!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"frequently-asked-questions\"><\/span>Frequently Asked Questions:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>1.What Is the Sum of Factors of 21?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"728\" height=\"362\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/183a551f-0121-4259-9156-24949b38f7be-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"1.What Is the Sum of Factors of 21?\" class=\"wp-image-57041\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/183a551f-0121-4259-9156-24949b38f7be-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 728w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/183a551f-0121-4259-9156-24949b38f7be-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-300x149.webp 300w\" sizes=\"(max-width: 728px) 100vw, 728px\" \/><\/figure><\/div>\n\n\n<p>The factors of 21 are 1, 3, 7, and 21. To find the sum of the factors, add them together: 1 + 3 + 7 + 21 = 32. Hence, the sum of the factors of 21 is 32.<\/p>\n\n\n\n<p><strong>2.What Is the Difference Between a Factor and a Multiple of 21?<\/strong><\/p>\n\n\n\n<p><strong>Factor:<\/strong> A number that divides 21 evenly. For example, 3 is a factor of 21 because 21 \u00f7 3 = 7.<\/p>\n\n\n\n<p><strong>Multiple:<\/strong> A number that is the result of multiplying 21 by another whole number. For example, 42 is a multiple of 21 because 21 \u00d7 2 = 42.<\/p>\n\n\n\n<p>Hence, factors divide 21, while multiples are the results of multiplying 21 by other numbers.<\/p>\n\n\n\n<p><strong>3.Is 21 a Square Number or a Composite Number?<\/strong><\/p>\n\n\n\n<p><strong>Square Number:<\/strong> A number that is the result of multiplying an integer by itself. For example, 16 is a square number because 4 \u00d7 4 = 16.<\/p>\n\n\n\n<p>21 is not a square number because no integer multiplied by itself equals 21.<\/p>\n\n\n\n<p><strong>Composite Number:<\/strong> A number that has more than two factors (1 and itself).<\/p>\n\n\n\n<p>21 is a composite number because it has four factors: 1, 3, 7, and 21.<\/p>\n\n\n\n<p>Hence, 21 is not a square number but is a composite number.<\/p>\n\n\n\n<p><strong>4.What are the multiples of 21?<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"362\" height=\"266\" src=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/6fde34de-b410-47ee-93c8-89fe15f34626-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp\" alt=\"4.What are the multiples of 21?\" class=\"wp-image-57042\" srcset=\"https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/6fde34de-b410-47ee-93c8-89fe15f34626-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800.webp 362w, https:\/\/wp-more.wukongedu.net\/blog\/wp-content\/uploads\/2025\/03\/6fde34de-b410-47ee-93c8-89fe15f34626-\u6700\u5927\u5bbd\u5ea6-2400-\u6700\u5927\u9ad8\u5ea6-1800-300x220.webp 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><\/figure><\/div>\n\n\n<p>Multiples of a number are obtained by multiplying that number by integers (1, 2, 3, 4, &#8230;).<\/p>\n\n\n\n<p>The multiples of 21 are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>21\u00d71=2121\u00d71=21<\/li>\n\n\n\n<li>21\u00d72=4221\u00d72=42<\/li>\n\n\n\n<li>21\u00d73=6321\u00d73=63<\/li>\n\n\n\n<li>21\u00d74=8421\u00d74=84<\/li>\n\n\n\n<li>21\u00d75=10521\u00d75=105<\/li>\n\n\n\n<li>And so on&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Hence, the multiples of 21 are <strong>21, 42, 63, 84, 105, &#8230;<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"mastering-factors-and-multiples\"><\/span>Mastering Factors and Multiples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Understanding how to identify factors is a core competency within the Common Core State Standards for Mathematics. This skill is primarily introduced in <strong>Grade 4 (4.OA.B.4)<\/strong>, where students learn to find all factor pairs for whole numbers in the range 1\u2013100. It is further refined in <strong>Grade 6 (6.NS.B.4)<\/strong> as students apply these concepts to find the Greatest Common Factor (GCF) and solve real-world problems.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Factor Reference Table<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>Number<\/strong><\/td><td><strong>Quick Link to Factor Guide<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>9<\/strong><\/td><td><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.wukongsch.com\/blog\/factors-of-9-post-40080\/\">Factors of 9<\/a><\/td><\/tr><tr><td><strong>10<\/strong><\/td><td><a href=\"https:\/\/www.wukongsch.com\/blog\/factors-of-10-post-43276\/\">Factors of 10<\/a><\/td><\/tr><tr><td><strong>21<\/strong><\/td><td>Factors of 21(this)<\/td><\/tr><tr><td><strong>24<\/strong><\/td><td><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.wukongsch.com\/blog\/factors-of-24-post-55796\/\">Factors of 24<\/a><\/td><\/tr><tr><td><strong>36<\/strong><\/td><td><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.wukongsch.com\/blog\/factors-of-36-post-43288\/\">Factors of 36<\/a><\/td><\/tr><tr><td><strong>48<\/strong><\/td><td><a target=\"_blank\" rel=\"noreferrer noopener\" href=\"https:\/\/www.wukongsch.com\/blog\/factors-of-48-post-55803\/\">Factors of 48<\/a><\/td><\/tr><tr><td><strong>60<\/strong><\/td><td><a href=\"https:\/\/www.wukongsch.com\/blog\/factors-of-60-post-40105\/\">Factors of 60<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"conclusion\"><\/span>Conclusion<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In this article, we explored the <strong>factors of 21<\/strong>, learning how to find them using division and multiplication methods. We also covered prime factorization, factor trees, and factor pairs, along with examples and tips to avoid common mistakes. Understanding factors is a key step in building a strong math foundation.<\/p>\n\n\n\n<p>Ready to take your math skills to the next level? Try <a href=\"https:\/\/www.wukongsch.com\/math\/\">WuKong Math<\/a>! Our interactive lessons make learning math fun and easy, helping you master concepts like factors and beyond. Join Wukong Math today and discover the joy of learning math!<\/p>\n\n\n<div class=\"retention-card-new\" data-lang=\"en\" data-subject=\"MATH\" data-btnName=\"Get started free!\" data-subTitle=\"Suitable for students worldwide, from grades 1 to 12.\">\r\n    <div class=\"retention-card-l\">\r\n        <div class=\"trustpilot-image\"><\/div>\r\n        <h3><p>Discovering the maths whiz in every child,<br \/>\n<span>that&#8217;s what we do.<\/span><\/p>\n<\/h3>\r\n        <p>Suitable for students worldwide, from grades 1 to 12.<\/p>\r\n        <a class=\"retention-card-button is-point\" href=\"https:\/\/www.wukongsch.com\/independent-appointment\/?subject=math&amp;l=eafd8b18-486b-4e0a-b93d-4105d41d2067&amp;booking_triggerevent=BLOG_DETAIL_MODEL_CTA_BUTTON\" data-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u70b9\u51fb\" data-event=\"C_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" data-expose-buttonname=\"\u7acb\u5373\u9884\u7ea6\u6309\u94ae\u66dd\u5149\" data-expose-event=\"D_Blog_BLOG_DETAIL_MIDDLE_CTA_BUTTON\" target=\"_blank\" title=\"Get started free!\">\r\n            Get started free!\r\n        <\/a>\r\n    <\/div>\r\n    <div class=\"retention-card-r\"><\/div>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>If you\u2019ve ever wondered what numbers can team up to create 21 through multiplication, you\u2019re in the right place.Factors are like building blocks of a number. For example, 3 and 7 are factors of 21 because when you multiply them (3 \u00d7 7), you get 21. In this article, Wukong Education will explore what all the factors of 21 are, how to find factors of 21 using simple methods like division and multiplication, and dive into concepts like prime factorization, factor trees, and factor in pairs. We\u2019ll also look at examples and discuss common mistakes to help you master the topic with confidence. What are the factors of 21? Understanding the factors of 21 is essential in mathematics, as it&#46;&#46;&#46;<\/p>\n","protected":false},"author":211806801,"featured_media":57044,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[134689],"tags":[],"class_list":["post-43333","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-math-learning"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Factors of 21:A Easy Guide From Concept to Practice - WuKong Edu Blog<\/title>\n<meta name=\"description\" content=\"Learn the factors of 21 with easy steps, a factor tree, prime factorization, examples, and practice tips. 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