# Factorials

Counting the possible ways that something can happen is a topic of some GMAT questions, and the mathematics of counting tends to involve factorials, which are labeled with an exclamation point, such as 5! or *n*!.

The factorial of an integer *n*, denoted by *n*!, is the product of all positive integers less than or equal to *n*. For example,

The value of 0! is 1, by definition.

As you can see, as *n *increases, the factorial of *n *increases very quickly.

Let’s look at the factorials of two adjacent numbers:

You can see here that 6! includes all of the factors of 5!. In fact, the factorial of 6 is just 6 times the factorial of 5. The factorial of any number equals that number multiplied by the factorial of the number one less than it. In other words,

## Practice Questions

Divisibility of a Large Number:

http://www.gmatfree.com/divisibility-of-a-large-number

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