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# Factorials Demystified

Dec 12, 2018

## What are factorials?

Factorials are among the more advanced math topics you'll be expected to know on the GMAT or GRE, especially if you're shooting for a high score. They most commonly come up in what I call "counting" questions (the "how many ways...?" questions that involve combinations and permutations), but you may see factorials tested individually as well.

You recognize a factorial by the exclamation point "!" after a number, and that mathematical notation simply tells you to multiply every integer in decreasing order starting with the number before the exclamation point and stopping at one (1).

For example, 8! (read "eight factorial") = 8x7x6x5x4x3x2x1 = 40,320.

## Advanced Factorial Example + Strategy

As you can see, factorials can get pretty big! And in fact, you very rarely actually need to multiply out all of the numbers to solve problems involving factorials on your exam. The numbers can get too large for the built-in calculator on the GRE, and you don't even have the luxury of a calculator on the GMAT. So there must be a better way, right?

There definitely is, and that's what I want to illustrate for you in this lesson.

A student recently came to me with the following question during one of our recent office hours sessions:

The expression n! is defined as the product of the integers from 1 through n. If p is the product of the integers from 100 through 299 and q is the product of the integers from 200 through 299, which of the following is equal to p/q?

(A) 99!
(B) 199!
(C) 199! / 99!
(D) 299! / 99!
(E) 299! / 199!

Give it a try and see how you do. Then watch the video for a detailed explanation where I'll teach you not only how to solve this particular question, but also some important tricks for simplifying factorials that will equip you for success on any factorial question the GMAT or GRE can throw at you.

Factorials don't have to be scary. Once you learn these few simple things, you'll not only welcome factorials questions on test day, but since they're considered to be harder questions by the test makers, you'll hopefully see a higher score as well.