Q: how do you prime factor 1021
A: see if the digits add up to 3, which they don't, then check for 7, so ditch the 21 and see if the 10 is a multiple of 7 which it's not, then check for 11 by subtracting it from 1021 which makes 101 (after you drop the zero at the end) and check if 101 is a multiple of 11 which you should know it's not because 101 is prime, then check for 13 by adding 39 to 1021 which makes 106 (after you drop the zero at the end) then divide by 2 to get 53 and check if that's a multiple of 13 which of course it's not because it's neighbor 52 already is, then check 17 by eliminating the 102 from the left of 1021 and you're left with 1 which is not a multiple of 17, then check 19 by adding it to 1021 and you get 104 (after dropping the zero at the end) and you probably already know 104 is not a multiple of 19 (divide it by 2 a few times and you'll just get to 13), then check 23 by adding 69 to 1021 to get 109 (after you drop the zero) which is prime so 23 is out, then check 29 by adding it to 1021 which makes 105 (after you drop the zero) which you might already know as just 7x15 so no 29s there, then you can check 31 by subtracting it from 1021 which makes 99 (after you drop the zero) and we all know that 99 is just 11x9 (without any 31s in it), then you can check 37 except i THINK we're already done because i think 37 squared is already higher than 1021 because 32 squared is 1024 (famously) so 37 squared can't be any lower than that. and if 37 squared is higher than 1021, then that means we're never gonna find any other prime factors higher than that, because, if we did, their partner factor would have to be something lower and we checked everything lower already, so 1021 is prime, so your answer is an earth shattering 1x1021