Factorial of a Number in Java

Basic Java Program

A factorial is a mathematical function denoted by an exclamation mark (!). It is defined for a non-negative integer n as the product of all positive integers less than or equal to n.

The factorial of n, written as n!, is calculated as:

n! = n × (n−1) × (n−2) ×…× 3 × 2 × 1

For example:

• 5! = 5 × 4 × 3 × 2 × 1 = 120
• 4! = 4 × 3 × 2 × 1 = 24
• 3! = 3 × 2 × 1 = 6
• 2! = 2 × 1 = 2
• 1! = 1
• 0! = 1 (by definition)

Factorial of numbers

import java.util.Scanner;

public class Factorial {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        
        System.out.print("Enter a number: ");
        int number = scanner.nextInt();
        
        int factorial = 1;
        
        for (int i = 1; i <= number; i++) {
            factorial *= i;   // factorial = factorial * i;
        }
        
        System.out.println("The factorial of " + number + " is " + factorial);
        
        scanner.close();   // Close the Scanner object to free up resources
    }
}

// Output:
      /*     Enter a number: 6
             The factorial of 6 is 720      */

The line int factorial = 1; is important because:

1. Multiplicative Identity:

• In multiplication, multiplying by 1 doesn’t change the value.
• For example, 5 * 1 = 5. So, starting with 1 means our first multiplication is correct and doesn’t affect the result.

2. Starting Point for Multiplication:

• If we start with factorial set to 0, any number multiplied by 0 will always be 0.
• For example, 5 * 0 = 0. So, if we start with 0, the result will always be 0, which is wrong.
• By starting with 1, we can correctly multiply all numbers in the sequence to get the factorial.

Example:

To calculate the factorial of 4 (4!), the steps are:

1. Start with factorial = 1.
2. Multiply factorial by 1 → factorial = 1 * 1 = 1.
3. Multiply factorial by 2 → factorial = 1 * 2 = 2.
4. Multiply factorial by 3 → factorial = 2 * 3 = 6.
5. Multiply factorial by 4 → factorial = 6 * 4 = 24.

So, 4! = 24.

Starting with 1 ensures that these multiplications work correctly. If we started with 0, every step would result in 0.

The statement factorial *= i; is a shorthand way of writing factorial = factorial * i;.

• factorial is a variable that holds the current value of the factorial calculation.
• *= is a compound assignment operator that means "multiply the current value by the specified value and store the result back in the variable."
• i is the loop control variable that changes with each iteration of the loop.