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Factorial CalculatorCalculate n! • Step-by-Step Solutions • Combinatorial Mathematics
Factorial Calculation
Step-by-Step
Combinatorics
Probability
Quick Test Numbers:
Combinatorial mathematics
Enter any non-negative integer between 0 and 170 to calculate its factorial
Factorial Mathematics Complete Guide
Factorial Properties
0! = 1: Mathematical definition for consistency in formulas
1! = 1: Base case of factorial function
n! = n × (n-1)!: Recursive definition of factorial
Super-exponential growth: Factorials grow faster than exponential functions
Key Applications
Permutations: nPr = n!/(n-r)! for ordered arrangements
Combinations: nCr = n!/(r!(n-r)!) for selections
Probability: Calculating probabilities in complex scenarios
Algorithm Analysis: Complexity analysis in computer science
Common Factorial Values
0! - 5!1, 1, 2, 6, 24, 120
6! - 10!720, 5040, 40320, 362880, 3628800
Large Factorials20! ≈ 2.43×10^18, 50! ≈ 3.04×10^64
Max in Tool170! ≈ 7.26×10^306