How to Find Factors of a Constant Term

Some people find a calculator useful in finding factors.
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The word “constant” is an algebraic term referring to a number that doesn’t have any variables, such as “x” or “y,” attached to it. (See Reference 1) For example, “-7” is a constant, but “-7x” is not. Essentially, constants are just regular numbers, so finding the factors of a constant term is akin to factoring any number. The concept of factoring is typically taught in late elementary or early middle school. When asked to find factors, the answer is simply a list of pairs of numbers that multiply to equal the number being factored.

    Write down the number “1” and the constant that you’re being asked to factor. This is your first factor pair, because 1 times any constant equals that constant. For instance, if you’re asked to factor “-12,” write down “1, -12.”

    Determine whether the number “2” is a factor of your constant. Essentially, you want to figure out if you can multiply 2 by some integer to equal your constant. In the case of -12, 2 is indeed a factor, as it can be multiplied by -6 to produce -12. So, in the example, your second factor pair is “2, -6.” If 2 doesn’t multiply evenly into your constant, as would be the case if you were factoring a number like 9, then don’t write anything down for this step.

    Determine whether the number “3” is a factor of your constant. As with ascertaining whether “2” was a factor, you need to figure out if you can multiply 3 by some integer to equal your constant. In the case of -12, 3 is also a factor, because it can be multiplied by -4 to equal -12. Hence, in the example, your third factor pair is “3, -4.” If 3 doesn’t multiply evenly into your constant, then don’t list any factors for this step.

    Continue in this manner, testing the next-largest integer to see if it is a factor, until you reach the constant. In the example, the rest of the factor pairs are: 4 and -3, 6 and -2, and 12 and -1. Thus, in total, the factors of -12 are: 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12 and -12. If you are factoring a positive number, you can stop testing factors when you begin encountering repeats. For example, if you’d been factoring 12 instead of -12, you could have stopped after testing “3” because any factors thereafter would have already been listed.

    Tips

    • Include only integers when factoring; do not list fraction or decimal numbers. Every constant has at least two factors: the number “1” and that constant. For example, “3” has exactly two factors: 1 and 3.

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