Factors

Updated June 26, 2019 | Infoplease Staff

A whole number that can be divided cleanly into another whole number is called a factor of that number.

You can also look at this the other way around: if you can multiply two whole numbers to create a third number, those two numbers are factors of the third.

You will notice that 1 and the number itself are always factors of a given number.

A Note About Negatives

Everything said above also applies to negative whole numbers.

• The factors of 10 are actually –1, 1, –2, 2, –5, 5, –10, and 10.

  (–1 x –10 = 10, and –2 x –5 = 10.)

• The factors of –10 are also –1, 1, –2, 2, –5, 5, –10, and 10.

  (2 x –5 = –10, –2 x 5 = –10, and so on.)

• This can be written more easily by using a combined + and – sign (±) to indicate that both the positive and negative versions of a number are factors. Thus, the factors of 10 can be written as ±1, ±2, ±5, and ±10.