What times what equils 221?

Answer 1

221 = 13*17
When looking for the prime factors of a number, you only need to check up to the square root of the number.

√221 = 14.86... so you only need to check up to 13 (the last prime before 14.86).

If a factor is greater than 14.86, then the other MUST be less than 14.86

So you try the list:
2, 3, 5, 7, 11, 13

we know it is not 2 (221 is not even)
we know it is not three (2+2+1 = 5 is not divisible by 3)
we know it is not 5 (221 does not end in 5 or 0)

only three left to check.