Greatest Common Divisor Calculator

Calculate the GCD of a set of numbers.

GCD Calculator Instructions

The GCD calculator allows you to quickly find the greatest common divisor of a set of numbers. You may enter between two and ten non-zero integers between -2147483648 and 2147483647. The numbers must be separated by commas, spaces or tabs or may be entered on separate lines.

Press the button 'Calculate GCD' to start the calculation or 'Reset' to empty the form and start again.

Like for many other tools on this website, your browser must be configured to allow javascript for the program to function.

What is the greatest common divisor?

The greatest common divisor (also known as greatest common factor, highest common divisor or highest common factor) of a set of numbers is the largest positive integer number that devides all the numbers in the set without remainder. It is the biggest multiple of all numbers in the set.

The GCD is most often calculated for two numbers, when it is used to reduce fractions to their lowest terms. When the greatest common divisor of two numbers is 1, the two numbers are said to be coprime or relatively prime.

How is the greatest common divisor calculated?

This calculator uses Euclid's algorithm. To find out more about the Euclid's algorithm or the GCD, see this Wikipedia article.

The GCD may also be calculated using the least common multiple using this formula:

$ GCD(a,b) = \frac{\left| a \cdot b \right|}{LCM(a,b)} $