## Finding factors

- Factors come in pairs
- The largest factor of a number is the number, the next largest is at most half the size of the number
- Use these facts to find the factors systematically

Students can shout out factors of a number easily enough. A systematic layout for finding factors is shown in the screen grab above – I owe this one to Sue Wilding. By listing the factors in pairs, starting from 1 on the left, you can be sure of finding all of the factors of a number. When you reach a point where the two factors are the same (square numbers) or close (other numbers) you know when to stop.

The red arrow is a suggestion I give students to ‘peel off’ the factors in order of size: the factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

### Factors and Multiples contrasted

Factors | Multiples |

Finite number of factors for any whole number | Infinite number of multiples |

Most factors are smaller than number – largest is number itself | Most multiples larger than number, smallest is number itself |

I usually get people to comment on the idea that you just add the number on to find the next multiple. I summarise by stressing the idea that

- factors are
**usually smaller**than the number - multiples are
**usually larger**than the number

### Odd number of factors

- Some numbers have an odd number of factors
- Try finding the factors of 36, 25, 81
- These are the ‘square’ numbers