Factorial Calculator – Find n! Instantly Online
Calculate factorials, see step-by-step solutions, and learn about factorial mathematics
Factorial Calculator
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Quickly calculate factorials with our optimized algorithm.
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About Factorials
What is a Factorial?
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.
For example: 5! = 5 × 4 × 3 × 2 × 1 = 120
Special Case
By definition, the factorial of 0 is 1: 0! = 1
This is known as the empty product, and it’s consistent with the combinatorial interpretation of there being exactly one way to arrange zero objects.
Applications
- Combinatorics: Calculating permutations and combinations
- Probability: Computing binomial coefficients
- Series expansions: Taylor series and mathematical analysis
- Computer science: Algorithm analysis and recursive functions
Growth Rate
Factorials grow at an extremely fast rate. For example:
- 10! = 3,628,800
- 20! ≈ 2.433 × 10¹⁸
- 50! ≈ 3.041 × 10⁶⁴
- 100! ≈ 9.333 × 10¹⁵⁷
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Step-by-Step Solutions
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