How do you find factor strings using prime factorization?

Answer 1

You look for a factor, divide for that factor, then look for additional factors. Here is an example: factor 52.

It is fairly obvious that one of the factors is 2 (any number that ends with 0, 2, 4, 6, 8 has 2 as a factor), so you divide 52 by 2:

52 = 2 x 26

Once again, 26 is an even number (a multiple of 2), so you split off another factor of 2:

52 = 2 x 2 x 13

13 is a Prime number; but if you don't happen to know that, you can try dividing it by 2, 3, 5, or 7 (testing those numbers is sufficient for any one-digit or two-digit number). Since there are no further factors, that's the final solution.