# What Is a Factor in Math?

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In math, a factor is a term that is a part of another term when multiplied, so the number one is a factor for all existing numbers. Understand factors as they relate to math with instructions from a college-level math teacher in this free video on geometry.

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## Video Transcript

So what is a factor in math? Hi, my name is Jimmy Chang, I've been teaching collegiate mathematics for 9 years and once you understand what the definition of a factor is, you'll be able to understand what some examples of factors in math really are. So here it is. A factor, sounds complicated, is a term that when multiplied, is part of another term including itself. In other words, it's a term that can be part of another term via multiplication or it could be part of itself. Here's a case in point, take for example the number 12. Let's do a little bit of a factor tree so you can figure out all the different factors. Now pick any two numbers you want. Let's just say 4 times 3. Now that means 4 and 3 are examples of factors but the thing is, you can break this down even further, 4 can be broken up as 2 times 2. So when you really think about it, some numbers that are factors of 12 are 4 and 3 but also 2, 2 and 3. Now there's other factors of 12 such as 12 and 1 and 6 and 2 because these are also parts of numbers that can give you 12, these, all 4 of these numbers can also be considered as factors. The number 1 is a factor of every number out there. Now from an algebra perspective, you can think of factors in this way, suppose you have x squared plus 3x. What are the different parts? Well an easy way to think about this is see what they have in common. As you can see, they both have an x that they share. So x is considered a factor. Let's think about the leftovers. X times what is x squared? That is x. X times what is positive 3x? Well the only way that can happen is positive 3. So the two parts or rather the factors are of x squared plus 3x, the two parts of the multiplication are x and x plus 3. So you can think of factors not just numbers but also algebraic expressions and variables. And I'm Jimmy Chang and that's an example as to factors in math.

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