Prime Factorization

Question

Pre-Algebra requires an understanding of some specialized Arithmetic. Without this understanding, a student will not be able to pass Algebra.

One important skill to have in order to perform this specialized arithmetic, is how to determine the Prime Factorization of a composite number.

Can a student of Prealgebra please tell me what the prime factorization of 66 is?

Answer 1

First of all, be familiar with the list of the lower prime numbers (positive whole numbers that can only be divided evenly by themselves or one). These are 2, 3, 5, 7 ,11, 13, etc. To do prime factorization, successively divide the given figure to be factored by the lowest prime that "works" (divides with no remainder) until you reach 1.

For example: the prime factorization of 24 is 24/2 = 12; 12/2 = 6; 6/2 = 3; 3/3 = 1 and you're done.

Prime factors of 24 are 2•2•2•3, or 2³•3. You can always check by multiplying them out. Answer should be 24.

For 66, its 66/2 = 33; 33/3 = 11; 11/11 = 1. Hence 2•3•11.

Answer 2

This is prime factorization for 66: 66 = 2·3·11