Example 1: Find the common factors of 36 and 28

If you need help on how to find prime factors of a number, please refer to article at the end of this article.

Step 1: Find factors of 36.

First determine the prime factorization of 36. 36 = 2 x 2 x 3 x 3.
The prime factors of 36 can be used to find all factors of 36. To begin, start with 1.

1 x 36 (next, list the first prime, 2)

2 x 18 (cover up the 2 in the factorization and multiply the remaining factors to find the other factor, 18)

3 x 12 (Is there a 3 in the prime factorization? Yes. Cover up the 3, and multiply the remaining factors to get 12.

4 x 9 (Is there a 4? Of course not, but can you multiply any of the numbers in the factorization together
to get 4? Yes, “2 x 2”. Thus, cover up “2 x 2”, and multiply the remaining factors to get 9.

Can you get a 5? No.

6 x 6 (Can you combine to prime factors to get 6? Yes. Cover up “2 x 3” and multiply the remaining factors to get 6.

Can you get a 9? Yes, but this is a factor already listed or a repeat. Thus, you have found all the factors.

So, the factors for 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Step 2: Find all the factors of 28

First determine the prime factorization of 28. The prime factorization of 28 = 2 x 2 x 7.
The prime factors of 28 can be used to find all factors of 28. To begin, start with 1.

1 x 28 (next, list the first prime, 2)

2 x 14 (cover up the 2 in the factorization and multiply the remaining factors to find the other factor, 14)

(Is there a 3 in the prime factorization? No)

4 x 7 (Is there a 4? Of course not, but can you multiply any of the numbers in the factorization together to get 4? Yes, “2 x 2”. Thus, cover up “2 x 2”, and multiply the remaining factors to get 7.)

Can you get a 5? No.

Is it possible to get a 6? No.

Is there a 7? Yes. (Cover up the 7 in the factorization and multiply the remaining factors to find the other factor, 4.)

Can you derive 8, 9, 10, 11, 12, or 13? No. (Continue until a factor has been repeated.)

Can you get a “14”? Yes, by multiplying 2 and 7, but the factor, 14, is already listed. Thus, you have found all the factors.

So, the factors for 28 are 1, 2, 4, 7, and 14.


Step 3: Identify the common factors.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 28: 1, 2, 4, 7, 14, 28

*****The common factors of 36 and 28 are 1, 2, and 4.