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The factorial of a nonnegative integer, n, is denoted by: n! and represents the product of all the positive integers less than or equal to n. By definition, 0!=1 and 1!=1.

Example: Find 5!


\(\displaylines{5! &=& (5)(4)(3)(2)(1) \\ &=& 120}\)

Example: Find 10!


\(\displaylines{10! &=& (10)(9)(8)...(3)(2)(1)\\
&=& 3628800}\)

Why is this important?

You might encounter factorials when studying probability, Taylor series (in a calculus class), or in a discrete mathematics course. 

Using Your Calculator

A standard scientific calculator should have a button on it (labeled n!) that calculates factorials. Depending on your calculator, you may need to hit this button before or after you enter the number whose factorial you wish to find. On some calculators, you may also have to hit the "2nd function" key, sometimes labeled "INV". To make sure you're using your calculator correctly, try finding 5! should get an answer of 120.