Factors

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.

Factors and FractionsPrime Factors

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