Free Online Calculator
Factorial Calculator
🧮 🔢 Factorial Calculator
Advanced calculator with modern responsive design.
Calculate factorials (n!) for any non-negative integer. The factorial of n is the product of all positive integers less than or equal to n.
📊 Factorial Calculation
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📊 Factorial Result
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📝 Calculation Steps
📚 About Factorials
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.
Formula:
- n! = n × (n-1) × (n-2) × ... × 2 × 1
- 0! = 1 (by definition)
- 1! = 1
Common Factorial Values:
| n | n! | Calculation |
|---|---|---|
| 0 | 1 | 0! = 1 (by definition) |
| 1 | 1 | 1! = 1 |
| 2 | 2 | 2! = 2 × 1 |
| 3 | 6 | 3! = 3 × 2 × 1 |
| 4 | 24 | 4! = 4 × 3 × 2 × 1 |
| 5 | 120 | 5! = 5 × 4 × 3 × 2 × 1 |
| 6 | 720 | 6! = 6 × 5 × 4 × 3 × 2 × 1 |
| 7 | 5,040 | 7! = 7 × 6! |
| 8 | 40,320 | 8! = 8 × 7! |
| 9 | 362,880 | 9! = 9 × 8! |
| 10 | 3,628,800 | 10! = 10 × 9! |
Applications:
- Combinatorics: Counting permutations and combinations
- Probability: Calculating probabilities in statistics
- Mathematics: Series expansions and mathematical analysis
- Computer Science: Algorithm analysis and recursive functions
Properties:
- Factorials grow very rapidly (factorial growth)
- n! = n × (n-1)! (recursive definition)
- Factorials are only defined for non-negative integers
- Large factorials require special handling due to size
About This Calculator
Use the Factorial Calculator to solve the supported mathematical calculation from the values entered.
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