Objective

Be able to write a number as the product of prime factors

Remember the prime numbers?

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ….

Here are the first ten prime numbers:

Why are they prime?

Each number has only two natural factors. In every case the two factors are the number itself and the number 1

The factors of 2 are 1 and 2

The factors of 3 are 1 and 3

Prime factor decomposition

Write the number 36 as the product of its prime factors

36

Think of two numbers which multiply together to give 36.

We could use 2 and 18

2 18 Now ask yourself, “are these prime numbers?”

Is 2 a prime number?Yes. So we can stop this part of our tree here.

Is 18 a prime number?No. So we carry on

2

2

9

3 3

2

3 336 = 2 x 2 x 3 x 3

36 = 22 x 32

Prime factor decomposition

Write the number 28 as the product of its prime factors

28

Think of two numbers which multiply together to give 28.

We could use 7 and 4

7 4Now ask yourself, “are these prime numbers?”Is 7 a prime number?

Yes. So we can stop this part of our tree here.Is 4 a prime number?No. So we carry on

2

7

22

28 = 2 x 2 x 7

28 = 22 x 7

2

Now try some interactive questions

Click here to begin

Objective

Be able to write a number as the product of prime factors

Objective

Be able to write a number as the product of prime factors