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Math Factor: Definition & Explanation

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  • 0:03 Definition
  • 0:34 Finding Factors
  • 2:12 Negative Factors
  • 3:20 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this lesson, you'll learn how you can find factors of both numbers and variables. Discover how one number can have many different factors. Learn how you can use factors to your advantage.

Definition

A math factor is a number you multiply with others to get to a desired number. Whatever numbers you use to multiply together to get to a number of your choice are factors. Say, for example, your desired number is 8. Think about the numbers you can multiply together to get to 8. One option is to use a 2 and a 4. You can then say that 2 and 4 are factors of 8. That sounds easy enough, but how do you find factors if the desired number is not an easy number like 8?

Finding Factors

To find factors of harder numbers, like, say, 108, we need to use a little bit of math. Don't worry, it's not that bad.

Let's think about what it means to be a factor. When something is a factor of something else, it is multiplied by other things to get to that desired number. So if we didn't know what possible factors there are, we can go backwards, so to speak, and use division to find what other numbers multiply together to get my desired number.

So, with the number 108, we look at it and say, 'Hey, wait a minute; that's an even number! We can divide it by 2 to find another factor. We know already that 2 is a factor of 108.' Isn't that nice? Let's find another one.

Oh, look at that! We've found another factor of 108, and that's 54. Now we have two factors of 108: 2 and 54.

What about 3? Let's see if 3 works.

math factor

Hey, that works too! We have two more factors of 108. Let's try dividing 108 by 4 to see what happens.

math factor

That worked. So now I have two more factors: 4 and 27 are also factors of 108. What about 5?

math factor

Oh no! That one didn't work. For it to be a factor, it has to divide evenly. Getting a decimal for an answer means the 5 doesn't divide evenly into 108. So 5 is not a factor.

We can continue in this manner and divide the 108 by 6, then 7, then 8, and so on to find even more factors. You can keep going until you see that your numbers are repeating. So, yes, it's a little bit of a guessing game. Of course, if you know your multiplication tables well, that will definitely help you out.

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