Factorial Calculator - Learn & Calculate Factorials Instantly

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Understanding Factorials

Master the concept of factorials with interactive examples

What is a Factorial?

Definition: A factorial of a positive integer n, denoted as n!, is the product of all positive integers less than or equal to n.

n! = n × (n-1) × (n-2) × ... × 2 × 1
Special Case: By definition, 0! = 1 (this is a mathematical convention that makes many formulas work correctly).

Examples

5! = 5 × 4 × 3 × 2 × 1 = 120

4! = 4 × 3 × 2 × 1 = 24

3! = 3 × 2 × 1 = 6

2! = 2 × 1 = 2

1! = 1

0! = 1 (by definition)

Interactive Factorial Calculator

Click "Calculate Factorial" to see the result!

Where Are Factorials Used?

Factorials are important in many areas of mathematics:

  • Combinatorics: Counting arrangements and combinations
  • Probability: Calculating probabilities of events
  • Calculus: Taylor series expansions
  • Statistics: Various statistical formulas

Quick Facts

  • Factorials grow very quickly! 10! = 3,628,800
  • The factorial of negative numbers is undefined
  • The symbol "!" was introduced by Christian Kramp in 1808
  • 20! is over 2 quintillion!

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