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Factoring Numbers Lessons

Every number has at least four factors (2 pairs). The first two are 1 and the number itself. The second two are -1 and the number with its opposite sign. Therefore the first 4 factors of 17 are:

  • 1 & 17
  • -1 & -17

The first four factors of -12 would be:

  • 1 & -12
  • -1 & 12

Unless you know that the number is prime (by referencing it with a prime number chart), finding other factors is a process of Trial and Error. All of the operations you'll need to find other factors can be done in your head or by using a pencil and paper, but using a calculator will speed things up a bit.

Factoring Numbers

Based on what you just learned, you know that the first two factors of 18 are 1 and 18. The second two factors are the exact opposite, -1 and -18.

Start with the number 2 then divide 18 by each number. If the result of the division is a number without any digits after the decimal (i.e. 5 or 3 not 4.2 or 3.4444), or without a remainder when using long division, then the number you divided by and the result (quotient) from that division are both factors. For example:

The above problem divides out evenly, therefore 2 and 9 are factors of 18. The opposites of 2 and 9 are -2 and -9, and they are also factors of 18.

As you can see above, 3 divides evenly into 18, therefore 3 and 6 are factors of 18. The opposites of 3 and 6 are -3 and -6 which are also factors.

The remainder of 2 indicates that the number 4 does not divide evenly into 18, therefore it is not a factor. The number five (below) is not a factor because it does not divide evenly either.

As you can see above, the result of 18 divided by 5 without the remainder is 3. Since we already divided 18 by 3 we can stop searching for factors here. The complete list of factors of 18 is shown below, in order from least to greatest:

(-18, -9, -6, -3, -2, -1, 1, 2, 3, 6, 9, 18)

Factoring Numbers Resources

Practice Problems / Worksheet
Test your skill at the worksheet for this lesson.

Factoring Calculator
Finds factors of positive and negative integers (whole numbers).

Next Lesson: Greatest Common Factors (GCF)
Find Greatest Common Factors for both numbers and algebraic terms.

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