How to Find All Factors of a Number

When you multiply two numbers together to get a third number, the first two numbers are called factors of the third number. For example, 3 times 5 equals 15. Therefore, 3 and 5 are factors of 15. In another example, 1 times 15 equals 15. Therefore, 1 and 15 are factors of 15. In fact, for every number, one and that number are factors of the number. The best way to find all the factors of a number is to approach the problem methodically. That way, you won't miss any of the factors.

Things You'll Need

• Paper
• Pen or pencil

Instructions

1. Write "1" on the left side of your paper. On the right side, write the number you are factoring. For example, if you are factoring the number 15, then write "15."

2. Decide if 2 is a factor of your number. Ask yourself if you can divide your number evenly by 2. If you are factoring 15, then 2 is not a factor because 15 divided by 2 equals 7 with a remainder of 1. If there is a remainder, the number is not a factor.

3. Decide if 3 is a factor of your number. In our example, 3 is a factor because 15 divided by 3 equals 5 with no remainder. Write "3" on your paper to the right of the "1" on the same line. Write "5" on your paper to the left of "15," also on the same line.

4. Notice that you are working from the edges of your paper towards the middle. Keep testing numbers and filling in your number line, moving towards the middle of the line, until you reach numbers you have already tested.

5. Decide if 4 is a factor. In our example, 4 is not a factor because it does not go evenly into 15.

6. Continue with the next number after 4, which is 5. In our example of factoring 15, you are finished, because you have already written "5" down on your paper. You have now found all the factors of 15.

References

• Free Math Help: Factoring Numbers
• Tim Bedley: Finding Factors of a Number (video)
• Strategy for Finding Factors (video)