Overview
Interactive factorial visualization and calculation tool with step-by-step animations
Factorial Calculator
Interactive factorial visualization and calculation tool.
Factorial Calculator
Visualization
Enter a number and click Calculate to see the visualization
Factorial Definition
The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n.
Recursive Definition
n! = n × (n-1)!
0! = 1 (by definition)
Iterative Definition
n! = 1 × 2 × 3 × ... × n
0! = 1 (by definition)
Mathematical Significance
Factorials play a crucial role in combinatorics, probability theory, and many areas of mathematics. The factorial of n represents the number of ways to arrange n distinct objects in a sequence.
Stirling's Approximation
For large values of n, calculating the exact factorial becomes computationally intensive. Stirling's approximation provides a good estimate:
n! ≈ √(2πn)(n/e)ⁿ
Gamma Function
The factorial function can be extended to non-integer values using the gamma function:
n! = Γ(n+1)