**The prime factorization of 48 is 2 x 2 x 2 x 2 x 3 or 2 to the 4th power x 3.** Prime factorization is also called integer factorization, and sometimes prime decomposition, and is the determination of the set of prime numbers that multiply together in order to become the original number.

Prime factorization can be taught by first starting with the number. Starting with 48, the student will need to think about what number can be used to divide the original problem number (48). The number used to divide the original problem number cannot be a number that leaves an uneven result such as 9, 48 divided by 9 is 5.333 and is not an even result. However, 48 divided by 2 is. 48 divided by 2 is 24. So students save the "2" and then continue onward with the number 24. 24 can also be divided by 2 to equal 12 so the "2" is saved again. Now, the student has 2 x 2 and the "12" left. The 12 can be divided by 2 to get 6. The student now has 2 x 2 x 2 and the "6" left. This 6 can be divided by 2 to get 3. Now the student has 2 x 2 x 2 x 2 and the "3" left. The 3 is a prime number and cannot be divided evenly by another number so the "3" is the final saved number. The full answer then is 2 x 2 x 2 x 2 x 3. This is the process that the student will go through in order to complete prime factorization.