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.