{"id":7574,"date":"2021-10-27T17:38:31","date_gmt":"2021-10-27T12:08:31","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7574"},"modified":"2021-11-27T17:31:14","modified_gmt":"2021-11-27T12:01:14","slug":"how-to-find-greatest-common-divisor-gcd-or-hcf","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/how-to-find-greatest-common-divisor-gcd-or-hcf\/","title":{"rendered":"How to Find Greatest Common Divisor (GCD or HCF)"},"content":{"rendered":"

Here you will learn concept of gcd ot hcf and how to find greatest common divisor or highest common factor of numbers and fractions with examples.<\/p>\n

Let’s begin –<\/p>\n

Concept of GCD or HCF<\/h2>\n

Consider two natural numbers \\(n_1\\) and \\(n_2\\).<\/p>\n

If the numbers \\(n_1\\) and \\(n_2\\) are exactly divisible by the same number x, then x is a common divisor of \\(n_1\\) and \\(n_2\\).<\/p>\n

The highest of all the common divisors of \\(n_1\\) and \\(n_2\\) is called as the GCD or HCF. This is denoted as GCD(\\(n_1\\), \\(n_2\\))<\/p>\n

How to Find Greatest Common Divisor (GCD)<\/h2>\n
\n

(a) Find the standard form of the numbers.<\/p>\n

(b) Write out all the prime factors that are common to the standard form of the numbers.<\/p>\n

(c) Raise each of the common prime factors listed above to the lesser of the powers in which it appears in the standard forms of the numbers.<\/p>\n

(d) The product of the results of the previous step will be the GCD of the numbers. <\/p>\n<\/blockquote>\n

Rule for finding HCF of Fractions<\/h2>\n

HCF of two or more fractions is given by:<\/p>\n

\n

\\(HCF of Numerators\\over LCM of Denominators\\)<\/p>\n<\/blockquote>\n

Example<\/span><\/strong> : Find the GCD of 150, 210, 375.<\/p>\n

Solution<\/span><\/strong> : We have the numbers, 150, 210, 375.<\/p>\n

1). Writing down the standard form of numbers.<\/p>\n

150 = \\(5 \\times 5 \\times 3 \\times 2\\)<\/p>\n

210 = \\(5 \\times 2 \\times 7 \\times 3\\)<\/p>\n

375 = \\(5 \\times 5 \\times 5 \\times 3\\)<\/p>\n

2). Writing Prime factors common to all the three numbers is \\(5^1 \\times 3^1\\).<\/p>\n

3). This will give the same result, i.e. \\(5^1 \\times 3^1\\)<\/p>\n

4). Hence, the HCF or GCD will be \\(5\\times 3\\) = 15<\/p>\n

Example<\/span><\/strong> : Find the GCD of 50, 75.<\/p>\n

Solution<\/span><\/strong> : We have the numbers, 50, 75<\/p>\n

1). Writing down the standard form of numbers.<\/p>\n

50 = \\(5 \\times 5 \\times 2 \\)<\/p>\n

75 = \\(5 \\times 5 \\times 3\\)<\/p>\n

2). Writing Prime factors common to all the two numbers is \\(5^1 \\times 5^1\\).<\/p>\n

3). This will give the same result, i.e. \\(5^1 \\times 5^1\\)<\/p>\n

4). Hence, the HCF or GCD will be \\(5\\times 5\\) = 25<\/p>\n

Some Other Rules for HCF<\/h2>\n

If the HCF of x and y is G, then the HCF of<\/p>\n

(i) x, (x + y) is also G<\/p>\n

(ii) x, (x – y) is also G<\/p>\n

(iii) (x + y), (x – y) is also G<\/p>\n\n\n

\n
Previous – How to Find Least Common Multiple (LCM) of Numbers and Fractions<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn concept of gcd ot hcf and how to find greatest common divisor or highest common factor of numbers and fractions with examples. Let’s begin – Concept of GCD or HCF Consider two natural numbers \\(n_1\\) and \\(n_2\\). If the numbers \\(n_1\\) and \\(n_2\\) are exactly divisible by the same number x, …<\/p>\n

How to Find Greatest Common Divisor (GCD or HCF)<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[62],"tags":[497,496,498,499],"yoast_head":"\nHow to Find Greatest Common Divisor (GCD or HCF) - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn concept of gcd (hcf) and how to find greatest common divisor (highest common factor) of numbers with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/how-to-find-greatest-common-divisor-gcd-or-hcf\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Find Greatest Common Divisor (GCD or HCF) - 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