Question

Describe two methods for finding the prime factorization of a number

Answer 1

By definition, a prime number is a whole number greater than or equal to 1 that is not divisible by any number other than 1 or the number itself. There are two methods of finding the prime numbers to a composite number: by factor tree, and by factoring. The two methods actually have the same concept. They just differ in the illustration for better understanding.

Factor tree is used by finding any pair of number whose product is the given number. If one of those numbers are not prime, find another pair again whose product is that number. It is repeated until all you have left are prime numbers. For example:
                               
                          64
                         /   \
                      4      16
                     /  \      /  \
                   2   2    4   4
                             / \   / \
                            2 2 2 2

Therefore, the prime factorization of 64 is 2×2×2×2×2×2. The next method is just factoring. For example:

64 = (16)(4) = (4×4)(2×2) = (2×2×2×2)(2×2)
64 = 2×2×2×2×2×2