Euclid’s Algorithm Calculator

First Number (a):

Second Number (b):

Results

The Greatest Common Factor (GCF) of is:

Calculation Steps

Step	Equation	a =	b =	Remainder (R)

How to Find the GCF Using Euclid’s Algorithm

Given two whole numbers where a is greater than b, do the division a ÷ b = c with remainder R.
Replace a with b, replace b with R and repeat the division.
Repeat step 2 until R = 0.
When R = 0, the divisor, b, in the last equation is the greatest common factor, GCF.

Since greatest common factor (GCF) and greatest common divisor (GCD) are synonymous, the Euclidean Algorithm process also works to find the GCD.