How to Find Greatest Common Divisor

The problem of finding the greatest common divisor ^{[1] X The source} of two or more numbers is fairly easy to do, but there are a few steps you need to take to work out the result. To find the greatest common divisor of two numbers, you need to factor both numbers using knowledge of the times table, and then determine the largest numbers that appear in both series of factors.

Table of Contents

Compare common factors

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/6/6b/Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg/v4-728px-Find- the-Greatest-Common-Factor-Step-1-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/6/6b/Find-the-Greatest-Common- Factor-Step-1-Version-2.jpg/v4-728px-Find-the-Greatest-Common-Factor-Step-1-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}

Find the factors of the number. You don’t need to know how to factorize primes to find the greatest common divisor. First, you need to find all the factors of each number.

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/0/0d/Find-the-Greatest-Common-Factor-Step-2-Version-2.jpg/v4-728px-Find- the-Greatest-Common-Factor-Step-2-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/0/0d/Find-the-Greatest-Common- Factor-Step-2-Version-2.jpg/v4-728px-Find-the-Greatest-Common-Factor-Step-2-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}

Compare the factors until you find the greatest common factor of the two numbers. That is the greatest common divisor.

Using prime numbers

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/a/a5/Find-the-Greatest-Common-Factor-Step-3-Version-2.jpg/v4-728px-Find- the-Greatest-Common-Factor-Step-3-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/a/a5/Find-the-Greatest-Common- Factor-Step-3-Version-2.jpg/v4-728px-Find-the-Greatest-Common-Factor-Step-3-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}

Break the number into primes. A prime number is a number greater than 1 that does not have any factors by itself. Examples of prime numbers are 5, 17, 97, 331 and so on.

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/9/90/Find-the-Greatest-Common-Factor-Step-4-Version-2.jpg/v4-728px-Find- the-Greatest-Common-Factor-Step-4-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/9/90/Find-the-Greatest-Common- Factor-Step-4-Version-2.jpg/v4-728px-Find-the-Greatest-Common-Factor-Step-4-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}

Find the common prime factors. Choose the common primes among the prime multiples just found. We can have many, one, or no common prime factors.

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/9/94/Find-the-Greatest-Common-Factor-Step-5-Version-2.jpg/v4-728px-Find- the-Greatest-Common-Factor-Step-5-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/9/94/Find-the-Greatest-Common- Factor-Step-5-Version-2.jpg/v4-728px-Find-the-Greatest-Common-Factor-Step-5-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}

Calculation: If there is only one common prime factor, it is the greatest common divisor. If there are more than one common prime factor, you multiply them all together to get the greatest common divisor.

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/8/8a/Find-the-Greatest-Common-Factor-Step-6-Version-2.jpg/v4-728px-Find- the-Greatest-Common-Factor-Step-6-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/8/8a/Find-the-Greatest-Common- Factor-Step-6-Version-2.jpg/v4-728px-Find-the-Greatest-Common-Factor-Step-6-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}

The example above illustrates this approach.

Advice

A prime number is a number that is only divisible by one and itself.
Did you know that the mathematician Euclid of the third century B.C. found an algorithm to find the greatest common divisor of two natural numbers or two polynomials?

Steps

Compare common factors

Using prime numbers

Advice

Related Posts