Understanding Factorials: Definition, Examples, and Special Cases

What is a Factorial?

A factorial is a mathematical operation denoted by the exclamation mark “!” following a positive integer. It represents the product of that integer and every positive integer below it down to one.

How to Compute a Factorial

For example, the factorial of 5 is calculated as follows:

5! = 5 × 4 × 3 × 2 × 1 = 120

Special Cases

Two exceptional values are often highlighted:

0! = 1 – By convention, the factorial of zero is defined as one.
1! = 1 – Since the product of a single integer is itself, 1! equals one.

Applications of Factorials

Factorials are fundamental in combinatorics, probability, and calculus, particularly in the expansion of series and the definition of the Gamma function.

Further Learning

Explore related mathematical concepts in our Phasor Mathematics Worksheet.

For more details, see Factorial on Wikipedia.

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