Greatest Common Factor of two or more numbers is a common factor of the numbers which is the greatest among all the common factors. Greatest Common Factor is also called as Highest Common Factor(HCF).

Consider the numbers 12 and 30.

The factors of 12 are 1, 2, 3, 4, 6, and 12

The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30

So, we get the common factors of 12 and 30 as 1, 2, 3, and 6. Among these, the number 6 is the greatest. So, 6 is called as the greatest common factor of 12 and 30.

The greatest common factor of two or more numbers can be defined as the highest factor common to both the numbers. It can be obtained by making a list of factors of the given numbers and finding the greatest one which is common to all.

For example, let us find the GCF of 32, 36 and 48.

These numbers can be factorized as follows:

32 = 2 x 2 x 2 x 2 x 2
36 = 2 x 2 x 3 x 3
48 = 2 x 2 x 2 x 2 x 3

Here, 2 is repeating twice in all the products of the numbers. Thus, the GCF of 32, 36 and 48 is 2 x 2 = 4.