Factorial Calculator
Note: Maximum input is 170 due to JavaScript number limitations
Result
How to Use
- Enter a non-negative integer (0 to 170)
- Click "Calculate Factorial" to see the result
- The calculator will show the factorial value and calculation steps
What is a Factorial?
The factorial of a non-negative integer n is the product of all positive integers less than or equal to n. It is denoted by n! and calculated as:
n! = n × (n-1) × (n-2) × ... × 2 × 1
Example: 5! = 5 × 4 × 3 × 2 × 1 = 120
Special case: 0! = 1
Properties of Factorials
| Property | Description | Example |
|---|---|---|
| Definition | Product of all positive integers up to n | 4! = 4 × 3 × 2 × 1 = 24 |
| Zero Factorial | 0! is defined as 1 | 0! = 1 |
| Recursive Definition | n! = n × (n-1)! | 5! = 5 × 4! |
Applications
- Permutations and combinations
- Probability calculations
- Taylor series expansions
- Combinatorial problems
- Statistical analysis
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