Factorial Calculator
Calculate factorials (n!) with step-by-step calculations and explanations. Perfect for combinatorics, probability, statistics, and mathematical calculations.
Calculate Factorial (n!)
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Common Factorial Calculations
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Factorial Calculations
A factorial (denoted as n!) is the product of all positive integers from 1 to n. It's a fundamental concept in mathematics, particularly in combinatorics and probability.
Factorial Formula
The factorial of a non-negative integer n is defined as:
Special cases: 0! = 1, 1! = 1
Example: 5! = 5 × 4 × 3 × 2 × 1 = 120
Common Factorial Values
| n | n! | Calculation | Use Case |
|---|---|---|---|
| 0 | 1 | 0! = 1 (by definition) | Empty set arrangements |
| 3 | 6 | 3 × 2 × 1 | Arranging 3 items |
| 5 | 120 | 5 × 4 × 3 × 2 × 1 | Arranging 5 items |
| 10 | 3,628,800 | 10 × 9 × ... × 1 | Arranging 10 items |
| 12 | 479,001,600 | 12 × 11 × ... × 1 | Calendar permutations |
- Combinatorics: Calculate permutations and combinations for arrangements
- Probability: Determine outcomes in probability problems and statistics
- Mathematics: Solve equations involving factorials and series
- Computer Science: Algorithm analysis and recursive function calculations
- Statistics: Calculate distributions and sampling arrangements
Frequently Asked Questions
What is a factorial?
A factorial (n!) is the product of all positive integers from 1 to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.
How do you calculate factorials?
To calculate n!, multiply all positive integers from 1 to n. For example: 4! = 4 × 3 × 2 × 1 = 24. Factorials grow very quickly as n increases.
What are factorials used for?
Factorials are used in combinatorics for calculating permutations and combinations, in probability theory, statistics, and various mathematical formulas and algorithms.