Factorial notation

Mathematicians use a special notation to show they are using the factorial of a number:

x!

The exclamation mark after the number (in this case x) shows that we want the factorial of x. The factorial of a number means that we want to find the product of multiplying the given number by all the whole numbers between it and, including, one:

x × (x - 1) × (x - 2) × ··· ×1 = x!

To give some examples with values, we could look at 3! and 10!

3! = 3 × 2 × 1 = 6

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3628800

As you can see, factorials get very large very quickly, and they save a lot of time in writing out.