How do you find the prime factorization of 108?

Answer 1

First, you need to memorize your primes...
{2, 3, 5, 7, 11, 13, 17, 19, 23, etc}

Secondly, know the trick that you can stop looking when you reach the square root of the number you are searching for (in this case, 11 is too large; 11 x 11 = 121 so 11 could never be a factor of 108.)

Then keep dividing by primes, smallest to largest
108 =
2 x 54
2 x 2 x 27
2 x 2 x 3 x 9
2 x 2 x 3 x 3 x 3

and you are done!