### Prime Factors in GMAT Quant

The GMAT is challenging no matter what, especially the Quant section. Using prime factors as a way to break down complex problems into more bite-sized chunks is a great strategy. Here's a brief description of prime factors and how to use them for a successful GMAT test!

## What Are Prime Factors?

Prime numbers are numbers that are only divisible by 1 and themselves. Prime factorization, then, is the process of breaking down numbers into their most straightforward prime number factors. Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and so on. For a quick example of prime factorization, let's use the number 36. The number 36 breaks down into 2x18, and 18 breaks down into 2x9. Using 2 no longer works with 9, but if you use 3, you get 3x3. So, the prime factorization of 36 looks like this: 2x2x3x3. Check your math by redoing that problem 2x2=4, 4x3=12, 12x3=36 – and there you have it.

## How to Use Prime Factorization on the GMAT

Prime factors can be used on many different math problems on the GMAT, including both problem-solving questions, and data sufficiency ones. Prime factorization is so efficient at breaking down large numbers into manageable, smaller ones that it should be one of your first thoughts on any question where it can be used. Here is a sample question from the GMAT Review Official Guide, 14th Edition (#219, p. 183.):

In a certain game, a large container is filled with red, yellow, green, and blue beads worth, respectively, 7, 5, 3, and 2 points each. A number of beads are then removed from the container. If the product of the point values of the removed beads is 147,000, how many red beads were removed?

(A) 5

(B) 4

(C) 3

(D) 2

(E) 0

Using the scratch pad provided during the GMAT, you would immediately begin finding the prime factors for 147,000. After some effort, you'd be able to come up with 2x2x2x3x5x5x5x7x7. Because there are two 7's in the prime factorization of 147,000, you now know that the only way to get to 147,000 is if there are two red beads removed. Your answer, therefore, is (D) 2.

## Master Prime Factors with EmpowerGMAT

Prime factors aren't only useful on the specific prime factor problems. You can also use them as a speedy way to get to the answers on multiple forms of GMAT questions. The industry-leading GMAT prep course developed by EmpowerGMAT is built to mimic the questions received on a typical GMAT test and is delivered by computer, just like the GMAT itself. This training course will provide you with dozens of opportunities to practice using prime factors as a way of solving problems. Start your one-hour free trial today!