Calculate N Factorial Java

What is Factorial?

The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. Factorials are commonly used in combinatorics, algebra, and probability calculations.

For example, 5! (5 factorial) is calculated as 5 × 4 × 3 × 2 × 1 = 120.

Factorial Formula

The factorial of a number n can be calculated using the following recursive formula:

This recursive definition is the basis for most factorial implementations in programming languages.

Calculate Factorial in Java

Here's a Java method to calculate factorial using recursion:

public class FactorialCalculator {
    public static long factorial(int n) {
        if (n < 0) {
            throw new IllegalArgumentException("Factorial is not defined for negative numbers");
        }
        if (n == 0 || n == 1) {
            return 1;
        }
        return n * factorial(n - 1);
    }

    public static void main(String[] args) {
        int number = 5;
        long result = factorial(number);
        System.out.println(number + "! = " + result);
    }
}

For iterative approach, you can use:

public static long factorialIterative(int n) {
    if (n < 0) {
        throw new IllegalArgumentException("Factorial is not defined for negative numbers");
    }
    long result = 1;
    for (int i = 2; i <= n; i++) {
        result *= i;
    }
    return result;
}

Factorial Examples

Let's calculate some factorial values:

• 0! = 1
• 1! = 1
• 2! = 2 × 1 = 2
• 3! = 3 × 2 × 1 = 6
• 4! = 4 × 3 × 2 × 1 = 24
• 5! = 5 × 4 × 3 × 2 × 1 = 120

These examples demonstrate how factorial grows rapidly with increasing n.

Factorial Applications

Factorials have several important applications in mathematics and computer science:

1. Combinatorics: Calculating permutations and combinations
2. Probability: Calculating probabilities in discrete distributions
3. Algebra: Expanding polynomials and solving equations
4. Number Theory: Analyzing divisibility and prime numbers
5. Computer Science: Implementing algorithms and data structures

Understanding factorial is essential for working with these mathematical concepts and their practical applications.