Factors

Updated February 21, 2017 | Factmonster Staff

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

Example: Factors of 1010 can be evenly divided by 1, as 10 1 = 10
10 can be evenly divided by 2, as 10 2 = 5
10 cannot be evenly divided by 3: 10 3 = 3.333
10 cannot be evenly divided by 4: 10 4 = 2.5
10 can be evenly divided by 5: 10 5 = 2
10 cannot be evenly divided by 6, 7, 8, or 9
10 can be evenly divided by 10: 10 10 = 1
The factors of 10 are 1, 2, 5, and 10.

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.

Example: Factors of 102 x 5 = 10, so 2 and 5 are factors of 10.
1 x 10 = 10, so 1 and 10 are also factors of 10.

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.
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