Factors and Multiples

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Factors and multiples are things you are going to use throughout your time in math and in life.

What is a Factor?

A factor is a number that is multiplied by another number (factor) to get the answer to a multiplication problem.

Factor * Factor = Answer

A factor can be divided evenly into its multiple.

What is a Multiple?

The multiple is the answer in a multiplication problem. The answer is sometimes also called the product.

So, the multiple is what you are looking for when you do many of your elementary and early middle-school multiplication problems.

Factor * Factor = Multiple

As we have mentioned, a factor divides evenly into its multiple, without any remainders.

So, what’s the difference between a multiple and a product? A multiple, as we have said, can be divided by its factors, evenly and there are no fractional or decimal remainders…while a product can be any answer, in general, to a multiplication problem.

7 * 8 = 56

  • 56 is a multiple of 7 and 8

  • 7 and 8 are both factors of 56.

Which Numbers are the Factors?

  • 9 and 5 are the factors

  • 4 and 8 are the factors

Which Number is the Multiple?

  • 30 is the multiple (it is a multiple of 6 and 5)

  • 15 is the multiple (it is a multiple of 5 and 3)

Summary

  • Factors are the number you multiply together to get an answer—they divide evenly into their multiples.

  • Multiples are the answers you get when factors are multiplied together—their factors divide evenly into them.

Danita Smith