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Step 3: Lis the divisors common to "a" and "b".Step 2: Find the divisors of positive integer "b".Step 1: Find the divisors of positive integer "a".The greatest common divisor of two numbers can be determined using the following steps: How do you find the Greatest Common Divisor of Two Numbers? It is also known as the highest common factor or greatest common factor. The greatest common divisor for any two positive integers (a, b) is the greatest factor which is common to both the integers a and b. What is the lowest common denominator of 8 and 9?įAQs on Greatest Common Divisor What does Greatest Common Divisor Mean?.

Topics Related to Greatest Common DivisorĬheck out these interesting articles to know more about the greatest common divisor (GCD) and its related topics. GCD (12, 10) = GCD (10, 2) = GCD (2, 0) = 2Įuclid's algorithm is very useful to find GCD of larger numbers, as in this we can easily break down numbers into smaller numbers to find the greatest common divisor. In quotient remainder form we can write 10 = 2 × 5 + 0 In quotient remainder form we can write 12 = 10 × 1 + 2 Solution: The GCD of 12 and 10 can be found using the below steps:

We repeat this process until we get the remainder as 0.Įxample: Find the GCD of 12 and 10 using Euclid's Algorithm.

Find the GCD (b, r) as GCD (b, r) = GCD (a, b).

If both a≠0 and b≠0, we write 'a' in quotient remainder form (a = b×q + r) where q is the quotient and r is the remainder, and a>b.

$gcd mathematica$

If b = 0, then GCD (a, b) = a as GCD (a, 0) = a.If a = 0, then GCD (a, b) = b as GCD (0, b) = b.Euclid's Algorithm for Greatest Common DivisorĪs per Euclid's algorithm for the greatest common divisor, the GCD of two positive integers (a, b) can be calculated as: