# 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 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.**

**See also:**