Greatest Common Factor or Greatest Common Divisor of two numbers (or more) is a mathematical concept that refers to the biggest positive number that can divide the two numbers. There are different methods that can be used for the calculation of GCF. But you can also use our **greatest common factor calculator** to cut the hassle.

But if you are still interested in finding out about these methods before using this **greatest common factor calculator**, here are the different methods used for the calculation of GCF.

Prime Factorization Method

The first method to calculate GCF is through prime factorization of all the numbers involved. Determining the common factors in them, and then multiplying all these factors will help in finding the GCD. Check out the example below for understanding the concept.

**EXAMPLE:
GCF(16, 88, 104)
16 = 2*2*2*2 = 24
88 = 2*2*2*11 = 23*11
104 = 2*2*2*13
GCF(16, 88, 104) = 2**

Prime Factorization method works fine for smaller numbers. However, for larger numbers it can quickly become tedious to find out the prime factors and then determine common factors.

Euclidean Algorithm

This is another method used for calculating the GCF. It is way more effective as compared to prime factorization. This method makes use of division algorithm along with observing that GCD of the two numbers can divide the difference of the two as well. You can check out the algorithm below:

**EXAMPLE:
GCF(a, a) = a
GCF(a, b) = GCF(a-b, b), when a > b
GCF(a, b) = GCF(a, b-a), when b > a
**

In practice:

1.For any two given positive integers a & b, subtract smaller number i.e. b from larger number i.e. a, to get c as resultant

2.Keep subtracting b from the bigger number a till the result gets smaller as compared to b.

3.Continue with b as larger number and subtract resultant c, repeating same process described in above step until you get 0 as remainder.

4.When you get 0 as remainder, GCF will be the remainder that get in step preceding that zero result.

How This Greatest Common Factor Calculator Works?

Now that you know how to calculate the GCF or greatest common factor for any two given numbers, you can simply use this **Greatest Common Factor calculator** for finding the result with a click of a button. Just enter the numbers in the given text area separated with a comma. Click the calculate button and GCF will be displayed right in front of you. You can use it in whatever application you want.

So, cut the hassle and use this **Greatest Common Factor calculator** to get the most accurate results.