 What you need to know

Things to remember:

• If a number has more than two factors it is called a “composite number”.
• If a number only has two factors, then it is called a “prime number”
• 1 isn’t prime, and it isn’t composite.

Before starting, we need to just quickly remind ourselves of what factors are:

A factor is a number that divides another number and gives a whole number. For example, because $32\div8=4$, then 8 is a factor of 32. This means that 4 is a factor of 32 as well. We call these two numbers, 4 and 8, a factor pair. We can also think of the factor pairs as multiplying:

$$4\times8=32$$

Previously we have look at prime numbers and found that they only had two factors, 1 and itself.

Prime Number                                Factors

2                                              1 and 2

3                                              1 and 3

5                                              1 and 5

7                                              1 and 7

11                                            1 and 11

13                                            1 and 13

17                                            1 and 17

19                                            1 and 19

So, we have a special name for numbers with 2 factors, but how about numbers with more than two factors? We call these “composite numbers”.

Composite Number                            Factors

4                                              1, 2, and 4

9                                              1, 3, and 9

12                                            1, 2, 3, and 4

18                                           1, 2, 3, 6, 9, and 18

26                                           1, 2, 13, and 26

So, these are clearly composite numbers because they have more than two factors.

Let’s look at a special case, 1:

Number                                   Factors

1                                               1

So, 1 only has one factor, itself. So, 1 isn’t prime and it isn’t composite.

Example Questions

Factors of 24

1          2          3          4          6          8          12        24

24 is a composite number.

Factors of 29

1          29