In Part A of this session, we looked for prime factors of numbers. Using this method, the prime factorization of 72 is 2 2 2 3 3, or 23 32. In Part B, we listed all the factors of the number 72 in ascending order: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Notice that these two lists are very different. The prime factorization, which the fundamental theorem of arithmetic says is unique, lists only the prime factors of 72 and lists each factor as many times as it appears.
In contrast, the list of all factors lists all numbers that are factors of 72, many of which are not prime. When doing problems, make sure to think about this distinction.