{"id":39838,"date":"2022-10-07T12:39:47","date_gmt":"2022-10-07T07:09:47","guid":{"rendered":"https:\/\/ischoolconnect.com\/blog\/?p=39838"},"modified":"2025-03-20T15:46:36","modified_gmt":"2025-03-20T10:16:36","slug":"what-is-a-co-prime-number-definition-properties-and-example","status":"publish","type":"post","link":"https:\/\/ischoolconnect.com\/blog\/what-is-a-co-prime-number-definition-properties-and-example\/","title":{"rendered":"What is a co-prime number? | Definition, properties, and example"},"content":{"rendered":"\n<p>Co-prime numbers have no common factor other than 1. A set of co-prime numbers must consist of at least two numbers. For example, 4 and 7 have only 1 as their highest common factor. Co-prime numbers are also formed by two composite numbers, 4 and 9. Keep reading to learn what is a co-prime number and its definition and examples.<\/p>\n\n\n\n<div data-tf-widget=\"O9K1jN42\" data-tf-iframe-props=\"title=How to fund your education\" data-tf-medium=\"snippet\" data-tf-hidden=\"utm_source=ORGANIC_SEARCH,utm_medium=Blog,utm_campaign=what-is-a-co-prime-number-definition-properties-and-example,hubspot_utk=xxxxx,hubspot_page_name=xxxxx,hubspot_page_url=xxxxx\" style=\"width:100%;height:400px;\"><\/div><script src=\"\/\/embed.typeform.com\/next\/embed.js\"><\/script>\n\n\n\n<h2 id=\"what-is-a-co-prime-number\" class=\"wp-block-heading\">What is a co-prime number?<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"500\" height=\"333\" src=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers.jpg\" alt=\"what is co prime number\" class=\"wp-image-39845\" srcset=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers.jpg 500w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-300x200.jpg 300w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-345x230.jpg 345w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-370x247.jpg 370w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-440x294.jpg 440w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-170x113.jpg 170w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption>Co Prime Numbers are a group of integers or numbers that share only the number 1 as a common factor.<br><\/figcaption><\/figure><\/div>\n\n\n<p>For example, x and y are two positive <a href=\"https:\/\/ischoolconnect.com\/blog\/bodmas-rule-everything-you-need-to-know-about-it\/\">integers<\/a> that are co-prime numbers if and only if they have one common factor, and thus HCF(x, y) = 1. In other words, co-prime numbers are a pair of numbers or integers with only one common factor, namely that their highest common factor (HCF) is 1. Co-prime numbers are also known as mutually prime numbers or relatively prime numbers. It is critical to have two numbers to form co-primes.<\/p>\n\n\n\n<h2 id=\"how-to-find-co-prime-numbers\" class=\"wp-block-heading\">How to find co-prime numbers?<\/h2>\n\n\n\n<p>Consider a pair of numbers; if no positive integer other than 1 can divide them, the pair is co-prime.<\/p>\n\n\n\n<p>Example 1- 21 and 22<\/p>\n\n\n\n<p>For numbers 21 and 22-<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Number<\/td><td>Factors<\/td><\/tr><tr><td>21<\/td><td>1, 3, 7<\/td><\/tr><tr><td>22<\/td><td>1, 2, 11<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Here, 21 and 22 share only one factor, which is 1. As a result, the HCF is 1, and they are co-prime.<\/p>\n\n\n\n<p>Example 2- 21 and 27<\/p>\n\n\n\n<p>For numbers 21 and 27-<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Number<\/td><td>Factors<\/td><\/tr><tr><td>21<\/td><td>1, 3, 7<\/td><\/tr><tr><td>27<\/td><td>1, 3, 9<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>In this case, 21 and 27 shares two factors, 1 and 3. They have an HCF of 3 and are not co-prime.<\/p>\n\n\n\n<h2 id=\"co-prime-numbers-list\" class=\"wp-block-heading\">Co-prime numbers list<\/h2>\n\n\n\n<p>Here is the list of co-prime numbers-<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Co-prime numbers with<\/td><td>Co-prime number pair<\/td><\/tr><tr><td>1<\/td><td>(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1,7), (1,8), (1, 22), and so on<\/td><\/tr><tr><td>2<\/td><td>(2, 3), (2, 5), (2, 7), (2, 9), (2, 11), (2, 13), (2, 15), and so on<\/td><\/tr><tr><td>3<\/td><td>(3, 4), (3, 5), (3, 7), (3, 10), (3, 11), (3, 15), (3, 22), and so on<\/td><\/tr><tr><td>4<\/td><td>(4, 5), (4, 7), (4, 9), (4, 11), (4, 13), (4, 15), (4, 17), and so on<\/td><\/tr><tr><td>5<\/td><td>(5, 6), (5, 7), (5, 8), (5, 9), (5, 11), (5, 12), (5, 14), and so on<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-1 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-100\"><a class=\"wp-block-button__link\" href=\"https:\/\/ischoolconnect.com\/blog\/math-formulas-for-class-an-overview\/\" target=\"_blank\" rel=\"noreferrer noopener\">Read more: Math formulas for class 10 | Here\u2019s everything you need to know about math formulas<\/a><\/div>\n<\/div>\n\n\n\n<h2 id=\"properties\" class=\"wp-block-heading\">Properties<\/h2>\n\n\n\n<p>Co-prime numbers have six main properties, which are as follows-<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The universal co-prime number is 1. You can combine 1 with any <a href=\"https:\/\/ischoolconnect.com\/blog\/math-formulas-for-class-an-overview\/\">number<\/a>, and both will be co-prime. For example, (1,2), (1,3), (1,8), (1,15), (1,532), (1,2568).<\/li><li>In a number sequence, the integer immediately following and preceding an integer are co-prime. Take, for example, the number 33; thus, the number next to 33, i.e., 34, is co-prime to 33; similarly, the number before 33, i.e., 32, is also co-prime to 33.<\/li><li>Because 0 is a factor less number, it is not co-prime with any other number.<\/li><li>Even numbers can never be coprime because they all share a common factor other than 1, which is 2.<\/li><li>If we add two co-prime numbers and multiply them, the resulting numbers are also co-prime. For example, 3+4 = 7, and 3 x 4 = 12, the results 7 and 12 have only one common factor, and thus they are co-prime.<\/li><li>An odd number and an even number are also co-prime. However, if the numbers have 0 and 5 at the ones or unit places, they are not co-prime because they have an HCF = 5.<\/li><li>Prime numbers are co-prime numbers. For example,&nbsp; (11,13); 11=1&#215;11 &amp; 13= 1&#215;13<\/li><\/ul>\n\n\n\n<h2 id=\"co-prime-and-twin-prime-numbers\" class=\"wp-block-heading\">Co-prime and twin prime numbers <\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" width=\"500\" height=\"333\" src=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-1.jpg\" alt=\"what is co prime number\" class=\"wp-image-39848\" srcset=\"https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-1.jpg 500w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-1-300x200.jpg 300w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-1-345x230.jpg 345w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-1-370x247.jpg 370w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-1-440x294.jpg 440w, https:\/\/ischoolconnect.com\/blog\/wp-content\/uploads\/2022\/10\/numbers-1-170x113.jpg 170w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption>The set of two numbers that have precisely one composite number between them is known as twin prime numbers.<br><\/figcaption><\/figure><\/div>\n\n\n<p>Co-prime numbers have an HCF of one. Twin prime numbers, on the other hand, are prime numbers that have a difference of two. For instance, 7 and 5 are twin prime numbers. The following points distinguish co-prime and twin prime numbers.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Co-prime number<\/td><td>Twin prime number<\/td><\/tr><tr><td>The difference between two co-primes can be any whole number.<\/td><td>The difference between two twin primes is always two.<\/td><\/tr><tr><td>Co-prime numbers can be either prime numbers or composite numbers.<\/td><td>Twin prime numbers are always prime numbers.<\/td><\/tr><tr><td>Co-prime numbers can be twin prime numbers or not.<\/td><td>All twin prime number sets are co-prime.<\/td><\/tr><tr><td>Any number can join 1 to form a coprime pair.<\/td><td>1 form a twin prime pair only with 3. For example, 1 and 3 as (3-1=2)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Co-prime numbers from 1 to 100<\/p>\n\n\n\n<p>The are several pairs of co-primes ranging from 1 to 100. Among them are-<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>(13, 14)<\/li><li>(28, 57)<\/li><li>(1, 99)<\/li><li>(2, 97)<\/li><li>(46, 67)<\/li><li>(75, 41)<\/li><\/ul>\n\n\n\n<p>Furthermore, any number with the combination of 1 can be written as a coprime pair, such as (22, 1), (31, 1), (4, 1), (90, 1), (1, 100). Many coprime numbers from 1 to 100 are defined in this manner.<\/p>\n\n\n\n<h2 id=\"key-takeaways\" class=\"wp-block-heading\">Key takeaways<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>The co-prime number does not have to be a prime number. It can also be a composite number.<\/li><li>Any two prime numbers given must be a Co-prime.<\/li><li>Sets of two even numbers can never be co-prime.<\/li><li>Any number can form a coprime pair with number one (one).<\/li><li>Any two consecutive numbers are indeed co-prime numbers.<\/li><li>Two even numbers can never be co-prime numbers<\/li><li>Co-prime numbers need not be prime numbers. For instance, 12 and 35 are co-prime numbers, even though 12 and 35 are not prime numbers.<\/li><\/ul>\n\n\n\n<p>Did you find this blog informative? If so, do express your thoughts in the comments below. <a href=\"https:\/\/ischoolconnect.com\/en\/contact-us\/\">Click here<\/a> to contact us for more information on what is a co-prime number. We would be happy to assist you with your queries.<\/p>\n\n\n\n<p>Liked this blog? Read next: <a href=\"https:\/\/ischoolconnect.com\/blog\/great-mathematicians-of-india\/\" target=\"_blank\" rel=\"noreferrer noopener\">10 great mathematicians of India<\/a><\/p>\n\n\n\n<h2 id=\"faqs\" class=\"wp-block-heading\">FAQs<\/h2>\n\n\n\n<p>Q1. <strong>What is the co-prime of 60?<\/strong><\/p>\n\n\n\n<p><strong>Answer-<\/strong> For example, 60 divides by two to yield 30, which divides by two to yield 15, which divides by three to yield five (another prime). Hence, 60 = 2 \u00d7 2 \u00d7 3 \u00d7 5.<\/p>\n\n\n\n<p>Q2. <strong>What is the smallest co-prime number?<\/strong><\/p>\n\n\n\n<p><strong>Answer-<\/strong> 2 is the smallest prime number. To be prime, a number must have only two aspects- 1 and the number itself.<\/p>\n\n\n\n<p>Q3. <strong>How do you check if two numbers are coprime?<\/strong><\/p>\n\n\n\n<p><strong>Answer-<\/strong> If the greatest common divisor of two numbers, X and Y, is 1, they are said to be Co-Prime or mutually prime.<\/p>\n\n\n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"What is the co-prime of 60?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"For example, 60 divides by two to yield 30, which divides by two to yield 15, which divides by three to yield five (another prime). Hence, 60 = 2 \u00d7 2 \u00d7 3 \u00d7 5.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"What is the smallest co-prime number?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"2 is the smallest prime number. 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Keep reading to learn what is a co-prime number [&hellip;]<\/p>\n","protected":false},"author":69,"featured_media":39855,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[1411],"tags":[2403],"class_list":["post-39838","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-academics","tag-co-prime-number"],"better_featured_image":{"id":39855,"alt_text":"What is a co-prime number? | Definition, properties, and example","caption":"What is a co-prime number? | Definition, properties, and example","description":"What is a co-prime number? | Definition, properties, and 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