Write 36 as a product of prime factors. Give your answer in index form.
First write down any two factors of 36 (numbers that multiply together to give 36). Let's use 2 x 18. We now need to break these numbers down into prime factors. 2 is already a prime number, so we only need to break down 18. We do for 18 what we did for 36: choose two numbers that multiply to give 18. We now have 2, 2, 9. 9 is still not a prime number, so we need to do the same for this. This gives us 2, 2, 3, 3. These are all prime numbers, so are the prime factors of 36. Finally, we need to write these in index form. 2 x 2 x 3 x 3 gives us 22 x 32. Tip: technically, you could initially say 1 and 36 are factors of 36, but then you will still need to break 36 down into factors at the next step! 2 is a good factor to use if the number is even when you are trying to find prime factors, as you then already have a prime number and have one less number to break down!
