How do you find the prime factorisation of a large number like 420?

You start by dividing 420 by whichever numbers you know that it is divisible by.

420 is obviously divisible by 10 so you can start with 10 x 42.

Then, you factorise 10 and 10 = 2 x 5, so now we know 420 = 2 x 5 x 42.

42 is an even number, so we can divide by 2. 2 x 5 x 2 x 21. 21 = 3 x 7.

Therefore:

420 = 2 x 5 x 2 x 3 x 7.

As 2, 3, 5 and 7 are all prime numbers the factorisation is almost complete. However, as we have 2 x 2, this is factorised as 2^2.

Then, we write the primes out in numerical order, starting with powers:

420 = 2^2 x 3 x 5 x 7.