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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.



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Content copyright © 2014 by Beverly Mackie. All rights reserved.
This content was written by Beverly Mackie. If you wish to use this content in any manner, you need written permission. Contact Beverly Mackie for details.

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