Greatest Common Factor

Whole numbers that are multiplied to find a product are called factors of that product.

For example: 6 = 2 x 3

6 is the product and 2 and 3 are factors of 6

GCF can be obtained by making a list of factors as follows:

1) List the factors of the given numbers.

2) Find the common factors.

3) Find the GCF

The largest of the common factors is the GCF

E.g.: To find the GCF of 4 and 8:

Factors of 4 = 1, 2 and 4

Factors of 8 = 1, 2, 4 and 8

1, 2 and 4 are the common factors of 4 and 8 where 4 is the largest of the common factors.

So, 4 is the required GCF

GCF can be obtained by Prime factorization method as follows:

1) Find prime factorization of the numbers.

2) Find the common prime factors.

3) Calculate the GCF (GCF) = Product of the common prime factors

E.g.: 4 and 8

Prime factorization of 4 = 1 x 2 x 2

Prime factorization of 8 = 1 x 2 x 2 x 2

Common prime factors = 2, 2.

So, GCF = 2 x 2 = 4

To find the greatest number that divides certain numbers, leaving some remainders, follow the steps listed below:

1) Subtract the remainders from the corresponding numbers.

2) The greatest number is the GCF of the numbers calculated above

GCF can be obtained by using a ladder diagram as follows:

1) Begin with the least prime factor that divides each number completely

2) Continue dividing until the given numbers have no common factors

3) Calculate the GCF.
(GCF is the product of all the factors with which the given numbers are divided)

Greatest Common Factor (GCF) is the largest of the common factors of two or more numbers

We may find the GCF by making a list, using prime factorization, or using a ladder diagram