Greatest Common Factor Calculator

Find the greatest commond factor (GCF) of two numbers with this GCF Calculator.

First Number:
Second Number:

Calculate the greatest common factor between two numbers.

What is the Greatest Common Factor?

The greatest common factor between two numbers is the largest
factor that both numbers are divisible by. Sometimes the greatest
common factor is also referred to as the greatest common divisor (gcd),
or the highest common factor (hcf).

For example, find the GCF of the two numbers 12 and 16:

The factors for 12 are 1, 2, 3, 4, 6 and 12. These are factors of 12 because
12 is divisible by all of these numbers.

The factors for 16 are 1, 2, 4, 8, 16.

The two numbers (12 and 16) share common factors (1, 2, 4).
The greatest of these is 4 and that is the greatest common factor.

Examples of Greatest Common Factors

The GCF of 18 and 21 is 3.

The GCF of 2 and 16 is 2.

The GCF of 10 and 15 is 5.

The GCF of 8 and 12 is 4.

The GCF of 14 and 21 is 7.

The GCF of 20 and 30 is 10.

The GCF of 11 and 22 is 11.

The GCF of 24 and 36 is 12.

The GCF of 12 and 18 is 6.

The GCF of 7 and 14 is 7.

Methods to find the Greatest Common Factors

There are three basic methods to find the GCF or greatest common factor. The first is to list the factors. The second is to use prime factorization. The third, and probably as much, or more time-consuming as listing the factors, is to draw diagrams to break out the factors.

For smaller number combinations, listing the factors is pretty easy. This is the process used in the example used in the calculator on this page.

Prime Factorization requires listing out the prime factors of two numbers, then multiplying the prime factors that they have in common. Using the numbers in our example, above, we list the prime factors of 12 as 2x2x3 and the prime factors of 16 are 2x2x2x2. The first set of two's is the common factors. Multiply those and you get 4 as the GCF.

To learn more about using diagrams to find the GCF, check out this video.

Uses of the Greatest Common Factor

There are two main uses for the greatest common factor. One use is in the calculations used to find the least common multple of two numbers. The other is using the GCF to reduce a fraction to it's simplest form.

Calculating Least Common Multiple using GCF

If using the equation LCM = (a*b) / GCF(a and b).

Let's use the numbers 8 and 12, with 8 being variable (a) and 12 as variable (b). By using the CalcuNation GCF Calculator, we know that the GCF of 8 and 12 is 4. So, our equation comes out to LCM = (8*12) / 4. This calculates out as LCM = 24.

Using GCF to reduce a fraction

For the fraction 33/99 the number 33 is the numerator and
99 is the denominator.

First, find the greatest common factor of the two numbers.
GCF = 33

Second, divide both the numerator and denominator by the GCF.

Numerator is found from 33/33 = 1
Denominator is found from 99/33 = 3

The fraction 33/99 reduced to the simplest form is 1/3.