Greatest Common Factor (GCF) Calculator

It is the largest positive integer that divides a set of numbers evenly without leaving a remainder. For example, the GCF of 12 and 18 is 6, because 6 is the biggest number that divides both.

First, break each number down into its prime factors. Then, find the prime bases that are common to all numbers. Multiply these common prime bases together using their lowest exponents found in the factorizations.

The Euclidean Algorithm is a fast method for two numbers. You divide the larger number by the smaller number and find the remainder. Then, replace the larger number with the smaller number, and the smaller number with the remainder. Repeat this division until the remainder is zero. The last non-zero remainder is the GCF.

No. A factor of a number must be less than or equal to that number. Therefore, the GCF of a set of numbers can never be larger than the smallest number in the set.

There is no difference. Greatest Common Factor (GCF), Greatest Common Divisor (GCD), and Greatest Common Measure (GCM) are all terms that describe the exact same mathematical value.