# Greatest Common Factor (GCF) Calculator

An online calculator to calculate the greatest common factor GCF of two integers.

## Definition of GCF

The greatest common factor (GCF) is the largest number that is factor to two or more numbers. To find the the GCF, we first express the two numbers as the product of prime factors and then select all the factors that are common to both numbers and multiply them.
Example 1
Find the CGF of 40 and 60
Solution
We first express 20 and 60 as the product of prime numbers
40 = 2 � 2 � 2 � 5
60 = 2 � 2 � 3 � 5
The common factors are 2 � 2 and 5
GCF of 40 and 60 = 2 � 2 � 5 = 20

## Use of GCF to Reduce Fractions

The GCF of the numerator and denominator of a given fraction may be used to reduce the fraction.
Example 2
Reduce the fraction 18 / 120
Solution
GCF of 18 and 120
12 = 2 � 3 � 3
120 = 2 � 2 � 2 � 3 � 5
GCF of 18 and 120 = 2 � 3 = 6
We now reduce the given fraction 18 / 120 by dividing the numerator 18 and denominator 120 by the GCG of 18 and 120 found above.
18 / 120 = 18�6 / 120�6 = 3 / 20

## Use of GCF to Factor Algebraic Expressions

Example 3
Factor completely 32 x + 24 y + 16 z.
Solution
Find the GCF of the coefficient 32, 24 and 16.
Express 32, 24 and 16 as product of prime numbers
32 = 2 � 2 � 2 � 2 � 2
24 = 2 � 2 � 2 � 3
16 = 2 � 2 � 2 � 2
GCF of 32, 24 and 16 = 2 � 2 � 2 = 8
Since we are factoring completely, we have to take the GCF as the common factor in the given expression. Hence
32 x + 24 y + 16 z = 8 (4 x + 3 y + 2 z)

## Use the GCF calculator

Enter the values in the two positive integers M and N then press enter.
 M = 12 N = 8 GCF (Greatest Common Factor) of M and N =