Find All Factors

Example 1: Find all the factors of 24

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

First determine the prime factorization of 24. The answer is 24 = 2 x 2 x 2 x 3.
The prime factors of 24 can be used to find all factors of 24. To begin, start with 1.

1 x 24 (next, list the first prime, 2)

2 x 12 (cover up the 2 in the factorization and multiply the remaining factors to find the other factor, 12)

3 x 8 (Is there a 3 in the prime factorization? Yes. Cover up the 3, and multiply the remaining factors to get 8.
4 x 6 (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 6.

Can you get a 5? No. Can you get a 6? Yes, but this is a factor already listed or a repeat. Thus, you have found all the factors.

Example 2: Find all the factors of 48

First determine the prime factorization of 48. The answer is 48 = 2 x 2 x 2 x 2 x 3.
The prime factors of 48 can be used to find all factors of 48. To begin, start with 1.

1 x 48 (next, list the first prime, 2)
2 x 24 (cover up the 2 in the factorization and multiply the remaining factors to find the other factor, 24)
3 x 16 (Is there a 3 in the prime factorization? Yes. Cover up the 3, and multiply the remaining factors to get 16.
4 x 12 (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 12.)

Can you get a 5? No.
6 x 8 (Can you get a 6? Yes, “2 x 3”. Thus, cover up “2 x 3”, and multiply the remaining factors to get 8.)

Can you get a “7”? No. Can you get an “8”? Yes, but this is a factor already listed or a repeat. Thus, you have found all the factors.