Short result:
Factorial Calculator
Result
Date publish: 16.09.2024
|
Author: Calcwizard
Understanding Factorials
A factorial, denoted by the symbol !, is the product of all positive integers up to a specified number. For instance, the factorial of 5 (written as 5!) is calculated as 5 × 4 × 3 × 2 × 1 = 120. Factorials are widely used in permutations, combinations, and various mathematical calculations.
Interesting Facts About Factorials
- The factorial of 0 is defined as 1 (0! = 1), which is a unique property in mathematics.
- Factorials grow very quickly; for example, 10! equals 3,628,800.
- Factorials are used in calculating probabilities, particularly in binomial coefficients.
How to Use the Factorial Calculator
To use the Factorial Calculator, simply input a non-negative integer, and the calculator will provide the factorial of that number. Below are some examples:
| Input (n) | Factorial (n!) |
|---|---|
| 0 | 1 |
| 1 | 1 |
| 2 | 2 |
| 3 | 6 |
| 4 | 24 |
| 5 | 120 |
| 6 | 720 |
| 7 | 5040 |
| 8 | 40320 |
| 9 | 362880 |
| 10 | 3628800 |
Applications of Factorials
Factorials are essential in various fields, including:
- Combinatorics: Used to calculate combinations and permutations.
- Probability: Helps in determining the likelihood of events.
- Mathematics: Fundamental in series expansions and calculus.
Understanding factorials can significantly enhance your mathematical skills and problem-solving abilities.
