How is finding the factors of a number different from finding the prime factorization of a number.

When finding factors of a number, you are just finding numbers that can factor into it. When finding the prime factorization, you are narrowing down the factors to the smallest factored numbers.

Ex:     40                 •The bolded numbers are the most simplified factors.
         /    \
       8     5
     /   \
   4    2          The prime factorization of 40 is 5 x 2^3.
  /  \
 2  2