GCD Calculator (Greatest Common Factor/Divisor)

Enter two integers into the calculator to determine the greatest common divisor between the two numbers, also known as the greatest common factor.

GCD Formula

The greatest common divisor formula is an interesting one to look at. In short, there is no quick mathematical formula that you can plug numbers into. Instead, an iterative process must be done to calculate the GCD.

This iterative process involves starting at the lowest of the two numbers and working down towards 1 to find the greatest number that each integer can be divided by.

GCD Definition

The greatest common divisor, also known as GCD for short, is a term used in mathematics to describe the greatest positive integer that can divide two numbers and result in two more integers. In other words, the greatest integer that results in a non-partial number when dividing two numbers by that integer.

The GCD is also known as the greatest common factor, or GCF for short.

How to calculate the GCD of two integers?

The following is a step-by-step guide on how to calculate the GCD between two integers.

Let’s take two integers 9 and 6. We will determine the GCD between these numbers.
As stated above, we must implement an iterative process in order to calculate the GDC.
The first step is to start at the lower of the two numbers and try to divide each integer by that number. So, 9/6=1.333 and 6/6= 1. In this case, 9/6 is not a positive integer so we must move down towards 1.
Next, this would have us trying the same process for integers 5 and 4. We find that neither of these numbers results in a positive integer either.

FAQ

What is GCD?

The greatest common divisor, also known as GCD for short, is a term used in mathematics to describe the greatest positive integer that can divide two numbers and result in two more integers.