In this activity, we will write numbers as the products of prime factors.

__Method__

All whole numbers, other than primes and the number 1, can be written as the product of their prime factors.

We find the prime factors of a number by successively dividing the number by its factor pairs.

__Example__

Write **1,800 **as the product of its prime factors.

The best way to find the prime factors is to divide 1,800 using a** factor tree**.

Start with 1,800 at the top of the tree and draw two branches coming from the top. This pair of branches will carry a factor pair that multiply together to make 1,800. Let's use **180 x 10**

Neither 180 nor 10 are prime numbers, so we draw a pair of branches coming from each of them.

180 could have **18 and 10 **as its factor pair.

10 would have** 5 and 2** as its factor pair. Both __5 __and__ 2 __are prime numbers, so we either circle or underline those two numbers - we can't go any further with those.

Now we go to the other factor pair of 18 and 10. Neither of them are prime numbers, so we need to draw a pair of branches from each of them.

18 could have** 9 and 2 **as its factor pair.

__2__ is a prime number, so we underline it.

9 is not a prime number but we'll come back to that in a minute!

10 would have **5 and 2 **as its factor pair, as we saw earlier. Both are prime numbers, so we underline both__ 5 __and__ 2.__

Finally, we go back to 9. We draw another pair of branches coming from 9 and put **3 and 3 **as the factor pair. 3 is a prime number, so we underline both __3 __and __3.__

Now we have broken 1,800 into its factors, we need to gather up all the underlined factors because they are all prime numbers.

We have 5, 2, 2, 5, 2, 3 and 3

So, we can write that 1,800 as a product of prime factors is: 5 x 5 x 3 x 3 x 2 x 2 x 2 (Remember that product means to multiply)

We can also write this as **1,800 = 5² x 3² x 2³**

Here is an example of a factor tree for the number 36, so that you can picture what they look like..

36 has been split into its factor pair of 4 and 9.

4 has been split into its factor pair of 2 and 2. Both are prime numbers, so they have been circled.

9 has been split into its factor pair of 3 and 3. Both are prime numbers, so they have been circled.

So, the prime factors of 36 are 2, 2, 3 and 3.

36 as a product of its prime factors is: 3 x 3 x 2 x 2 or 3² x 2²

Let's have a go at some questions now.

You can look back to this explanation at any time during the activity by clicking on the red button at the side of the screen.