Factors
Updated February 21, 2017 | Factmonster Staff ![]( "Updated by an Factmonster Editor on February 21, 2017")
A whole number that can be divided cleanly into another whole number is called a factor of that number.
| Example: Factors of 10 | 10 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 10 | 2 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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