Factorial Calculator
Calculate the factorial of any positive integer with step-by-step solution
Examples
Example 1
For a positive integer n, the factorial is calculated as:
n! = n × (n-1) × (n-2) × ... × 3 × 2 × 1
Special cases: 0! = 1 (by definition) OR 1! = 1
Formula
n! = n × (n - 1) × (n - 2) × (n - 3) × ... × 1
How it works:
- A factorial (n!) multiplies all whole numbers from the given number (n!) down to 1
- Start with 𝑛 n, multiply it by 𝑛 − 1 n−1, then 𝑛 − 2 n−2, continuing until reaching 1
- 0! is defined as 1 by convention
Benefits & Features
Our factorial calculator helps you compute factorials quickly and understand the calculation process with detailed step-by-step solutions.
Key Features
- Instant factorial calculation
- Step-by-step solution display
- Support for large numbers
- Clear mathematical notation
- User-friendly interface
Common Applications
- Mathematics and statistics
- Probability calculations
- Combinatorics problems
- Scientific computations
- Educational purposes
Frequently Asked Questions
A factorial (denoted by !) is the product of all positive integers less than or equal to a given number. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120. By definition, 0! = 1.
0! is defined as 1 by mathematicians for several reasons: 1) It makes many mathematical formulas work correctly, 2) It follows from the combinatorial interpretation of factorials, and 3) It maintains consistency in mathematical patterns.
Due to JavaScript number limitations, this calculator can accurately compute factorials up to 170!. Beyond this, the results become too large for precise representation in standard JavaScript numbers.
Factorials are used in many areas: 1) Probability and statistics for calculating permutations and combinations, 2) Computer science for algorithm analysis, 3) Physics for quantum mechanics calculations, 4) Biology for genetic sequence analysis.
No, factorials are not defined for negative numbers in standard arithmetic. However, there is a related function called the Gamma function that can be used to calculate factorials for non-integer and negative numbers in advanced mathematics.