## What you need to know

Things to remember:

• Factors come in pairs, unless it is a square number.
• A number always has 1 and itself as factors, so we start with these.
• To make sure you have a factor, if you divide the original number by it and get a whole number answer, then it is a factor.

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:

$$4\times8=32$$

Factors of 32:

1          2          4          8          16        32

Two important points about factors we need to know are:

• 1 and the original number are always factors.
• Factors come in pairs (apart from a square number).

Find the factors of 48

Step 1: Start with the 1 and the number you started with.

1          2          3          4          6          8          12        16        24        48

Step 2: Work from the outside in looking for factor pairs.

It is usually best to start with smaller number 2, 3, 4, etc and divide your starting number by them to find if they are factors and their factor pair.

1                                                                                                           48

1          2                                                                                  24        48

1          2          3                                                          16        24        48

1          2          3          4                                  12        16        24        48

1         2          3          4          6          8          12        16        24        48

Finding factors in this way is useful for two reasons:

• Increasing the size of the factors from 1 makes sure you get all the factors.

When you get to the middle, like with 6 and 8, you just have to check the numbers between them to see if anything in between could be factors.

Find the factors of 64

1                                                                      64

1          2                                              32        64

1          2          4                      16        32        64

1          2          4          8          16        32        64

64 is special, when we got to the middle, we didn’t have a pair, there is just one number. This always happens with square numbers, there will be one number by itself!

Is 12 a factor of 60?

We’ve look at factors and how we find them, but how can we check to see if a number is a factor? Well, we have said that factors are numbers that divide another number and give a whole number, so let’s see if we get one.

$$60\div12=5$$

We got a whole number, so 12 is a factor of 60!

Is 4 a factor of 78?

$$78\div4=19.5$$

We didn’t get a whole number, so 4 isn’t a factor of 78.

## Example Questions

#### Question 1: Find the factors of 80

1                                                                                                          80

1          2                                                                                  40        80

1          2          4                                                          20        40        80

1          2          4          5                                  16        20        40        80

1          2          4          5          8          10        16        20        40        80

#### Question 2: Is 9 a factor 49?

$$49\div9=5.\overline{4}$$