# Maths Topic 07 - Factors: Divisibility rules, & prime factors

Factors: Divisibility rules & Prime Factors are maths skills that are commonly tested in 11+ exams and Selective School exams in the UK.

## Examples

### Example Question 1:

What are the prime factors of 48?

Answer: 2 and 3

Explanation: The factors of 48 are 1 & 48, 2 & 24, 4 & 12, 3 & 16 and 6 & 8. Of these factors only the numbers 2 and 3 are prime numbers and therefore are also the prime factors of 48. These prime factors can be multiplied by each other to make all of the factors of 48 e.g. 12 = 3 × 4 and 16 = 2 × 2 × 2 × 2.

### Example Question 2:

Using your knowledge of the rules for divisibility, find all of the factors of 108.

Answer: 1 & 108, 2 & 54, 3 & 36, 4 & 27, 6 & 18 and 9 & 12,

Explanation: Apply your knowledge of how to check if a number is divisible by a given number:

2 is a factor as 108 is an even number (ends with a 0, 2, 4, 6, or 8). 3 is a factor because if you add up all of the digits in 108 = 1 + 0 + 8 = 9, which is divisible by 3. 9 is a factor because if you add up all of the digits in 108 = 1 + 0 + 8 = 9, which is divisible by 9. 4 is a factor because if you look at the last 2 digits  (08) they are divisible by 4. 6 is a factor because 108 is divisible by both 2 and 3. Once you know one of a factor pair you can then easily work out the other number that it is multiplied by to make 108 e.g. 4 x ? = 108 .