### What are factors?

The factors of a number **divide exactly** in to it with no remainder

The factors of 12 are:

1, 2, 3, 4, 6 and 12

This is because they all divide the number 12 exactly with no remainder:

12 ÷ 12 = 1 (so **1** and **12** are factors of 12)

12 ÷ 2 = 6 (so **2** and **6** are factors of 12)

12 ÷ 3 = 4 (so **3** and **4** are factors of 12)

No other numbers will **divide exactly** in to 12, only its factors.

The factors of 16 are:

1, 2, 4, 8 and 16.

16 ÷ 1 = 16 (so **1** and **16** are factors of 16)

16 ÷ 2 = 8 (so **2** and **8** are factors of 16)

16 ÷ 4 = 4 (so **4** is a factor of 16)

### Working out Factors

To work out all the factors of a number you must divide it by each number up to half its value, starting at 1.

There are a few rules you should know about finding factors to make life **easier**:

**All numbers**have the factors 1 and themself.**All even numbers**have the factors 2 and half of themself.- Once you have found out that a number is a factor of another number, you
**don’t**need to divide by it again. So in the example below where we find the factors of 15, once we know 5 is a factor of 15 by dividing 15 by 3, we can then**skip**dividing 15 by 5 when we get to it – as it will just give us the factors 5 and 3 again.

Look at the example below to see how we find the factors of a number.

Example

**Question**: What are the factors of 15?

To work out the **factors** of 15 we must start off dividing 15 by 1 and work our way through each number from 1 up to 7.

Why 7, you ask? Well, **half** of 15 is 7.5 – half-way between 7 and 8. But as 8 is **over** half the value of 15 there is no point seeing if it is a factor so we stop at the number just under half the value, in this case 7.

As we go through each number we can note down the numbers that **divide exactly** as these are the **factors** of 15:

15 ÷ 1 = 15 (so **1** and **15** are factors of 15)

15 ÷ 2 = doesn’t go exactly so 2 is not a factor of 15

15 ÷ 3 = 5 (so **3** and **5** are factors of 15)

15 ÷ 4 = doesn’t go exactly so 4 is not a factor of 15

15 ÷ 5 = 3 (we can skip this as we already knew 5 and 3 were factors)

15 ÷ 6 doesn’t go exactly so 6 is not a factor of 15

15 ÷ 7 doesn’t go exactly so 7 is not a factor of 15

Now we have the factors of 15:

1, 3, 5 and 15.

### Common Factors

If you are asked to find the **common** factors of two or more numbers you must find out which factors are **the same** for these numbers.

Example

Question: What are the common factors of 12 and 16?

The factors of 12 are:

1, 2, 3, 4, 6 and 12.

The factors of 16 are:

1, 2, 4, 8, and 16.

So the **common** factors are:

1, 2 and 4.

### Prime Numbers

**Prime numbers** are special numbers that only have two factors, the number itself and 1.

For example, 3 is a **prime number**. It’s **only two factors** are 1 and 3.

5 is also a **prime number**, it’s **only two factors** are 1 and 5.

- 1 is
**not**a prime number, it does not have only two factors it has only one. - The
**only**prime number that is**even**is 2.