Factorials Calculator

What is a Factorial?

A factorial is the product of all positive integers less than or equal to a given positive integer. It is denoted by the symbol "!" after the number. For example, 5! (read as "5 factorial") means 5 × 4 × 3 × 2 × 1.

How to Calculate Factorials

To calculate a factorial, multiply the given number by all positive integers below it, down to 1. This operation is commonly used in combinatorics, algebra, and probability theory.

Formula

The formula for calculating the factorial of a positive integer n is:

\[ n! = n \times (n-1) \times (n-2) \times ... \times 3 \times 2 \times 1 \]

By definition, 0! = 1 and 1! = 1.

Calculation Steps

1. Start with the given number n
2. Multiply n by (n-1)
3. Multiply the result by (n-2)
4. Continue this process, multiplying by each integer down to 1
5. The final product is n!

Example

Let's calculate 5!:

1. Start with 5
2. 5 × 4 = 20
3. 20 × 3 = 60
4. 60 × 2 = 120
5. 120 × 1 = 120

Therefore, 5! = 120