Factorial Calculator
Easily compute factorials with our factorial calculator. Enter any number to quickly find its factorial and simplify complex mathematical calculations.
What is Factorial?
The factorial of a number n (written as n!) is the product of all positive integers less than or equal to n. For example: 5! = 5 × 4 × 3 × 2 × 1 = 120.
Factorial Formula
Factorial
Example Calculations
Factorial Calculator
A factorial calculator computes the product of all positive integers up to a given number.
Mathematically: n! = n × (n−1) × (n−2) × ... × 2 × 1
Real-Life Example
Suppose you want to calculate the factorial of 5:
- 5! = 5 × 4 × 3 × 2 × 1 = 120
- Factorial of 3: 3! = 3 × 2 × 1 = 6
- Factorial of 0: 0! = 1 (by definition)
Key Insight
Factorials are widely used in permutations, combinations, probability, and algebra. For example, there are 120 ways to arrange 5 distinct books on a shelf, which is 5!.
Why Factorials are Important
Factorials are essential in combinatorics, probability, and statistics. They are used in formulas for permutations, combinations, binomial expansions, and in advanced areas such as calculus and series expansions.
Applications of Factorials
- Counting permutations and combinations.
- Probability theory and statistical modeling.
- Expanding series in calculus (e.g., Taylor series).
- Solving recurrence relations and algebra problems.
- Computer science for algorithm analysis.