How do you use prime factorization to find the greatest common factor?

Answer 1

1) Get the prime factors for each number.

2) In the result, include all the prime factors that appear in ALL the numbers.

If a prime factor appears in different powers, use the lowest power.

Example 1:

14 = 2 x 7

21 = 3 x 7

The only common factor is 7.

Example 2:

12 = 22 x 3

80 = 24 x 5

Use 22 as the common factor.

Answer 2

Once you have a list of the prime factors of each of the numbers, identify the prime factors they have in common. Then multiply the prime factors they have in common to obtain the greatest common factor.

First, you have to find prime factors of both numbers.

Let's consider the pair of 210 and 315:

210 = 2 * 3 * 5 * 7

315 = 5 * 7 * 9

You have to find factors that appear in both factorizations and multiply them together to get the greatest common factor.

The prime factors that appear in both factorizations are 5 and 7.

The greatest common factor of 210 and 315 will be then 5 * 7 = 35.
Example: 30 and 42

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF