Introduction

A prime number is any number with no divisors other than itself and 1, such as 2 and 11. Any number can be written as a product of prime numbers in a unique way (except for the order).

Factors

A factor is a whole number that divides exactly into another whole number.
If a number can be expressed as a product of two whole numbers, then the whole numbers are called factors of that number.
So, the factors of 20 are 1, 2, 4, 5, 10 and 20.

Example 5
List all the factors of 42.

Solution:
the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
What are the factors of 12? Try making 12 in different ways.
Your answer should look like this:
6 x 2 = 12
12 x 1 = 12
4 x 3 = 12

Remember that you can write your numbers in any order you like for a multiplication so:
2 x 6 is the same as 6 x 2
1 x 12 is the same as 12 x 1
3 x 4 is the same as 4 x 3.

The full list of factors of 12 is 1, 2, 3, 4, 6, and 12.

Some numbers have many factors, so it is a good idea to work in an organised way or you may miss some. Don't forget to include 1 and the number itself in your list.

Here is one way to find the factors of 48. Start with 1 and pair off your numbers.

1 x 48, 2 x 24, 3 x 16, 4 x 12 and 6 x 8 all make 48.
Write the list in order: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Here is another way: Write your first pair of factors with a reasonable space between them, then move on to the next pair until you have them all.

1,2 3,4 6,8 12,16 24,48

Common Factors
Factors that are common to two or more numbers are said to be common factors.

Multiples

Multiples of a number can be made by multiplying the number by any whole number. The first four multiples of 2 are 2, 4, 6 and 8. You get them by doing 2 x 1, 2 x 2, 2 x 3 and 2 x 4

The numbers you find in the 2-times table are all multiples of 2.

Reminder: when you do multiplication you can write the numbers in any order and get the same answer. 6 x 2 is the same as 2 x 6.

Here is how to make multiples of 10. Just multiply 10 by a whole number each time.
1 x 10 = 10,
2 x 10 = 20,
3 x 10 = 30,
4 x 10 = 40,
5 x 10 = 50,
6 x 10 = 60,
and so on ...

The first six multiples of 10 are 10, 20, 30, 40, 50 and 60.

Example 1

Is 12 a multiple of 3?
If you multiply 3 by 4 you get 12, so 12 is a multiple of 3.

Example 2
20 is a multiple of 5 because 4 x 5 = 20.
20 is a multiple of 4 too, because 5 x 4 = 20.

Example 3

Is 15 a multiple of 3?
3 x 5 = 15. So 15 is a multiple of 3, (and also of 5).

Example 4

Is 21 a multiple of 6?
21 is not a multiple of 6 because you can't make 21 by multiplying 6 by any whole number.
6 x 3 = 18 and 6 x 4 = 24 but there is no whole number between 3 and 4 that could give us an answer of 21.

Example 5

Is 30 a multiple of 15?
30 = 2 x 15, so 30 is a multiple of 15.
You can also see that 2 x 3 x 5 = 30 so 30 is a multiple of 2, 3 and 5.
And 30 = 3 x 10 so 30 is a multiple of 10.
Also 30 = 5 x 6 so 30 is a multiple of 6 too.