Factorial of a number

Factorial of a non-negative number is the multiplication of all positive numbers that are smaller than are equal to n.

Formula: n! = n*(n-1)\(n-2)*... 2\1

n=5 => 5*4*3*2*1

n=5 => 1*2*3*4*5

factorial of 5 is 120

0! = 1

Factorial using for loop:

public class Factorial {
  public static void main(String[] args) {
    int n= 5, fact=1;

    for(int i=1;i<=n;i++){
      fact = fact * i;
    }
    System.out.println(n+" Factorial is "+fact);
  }
}

5 Factorial is 120

In the for loop we can start the loop from 2 also because 1*n =n. so 1*2= 2.

i=1 => 1<=5 => fact = 1 * 1=1

i=2 => 2<=5 => fact = 1 * 2=2

i=3 => 3<=5 => fact = 2 * 3=6

i=4 => 4<=5 => fact = 6 * 4=24

i=5 => 5<=5 => fact = 24 * 5 = 120

output: 120

Factorial using while loop:

public class Factorial {
  public static void main(String[] args) {
    int n= 5, fact=1;

    //It print the n value and the cursor it at the same line.
    System.out.print(n);
    while(n!=0){
      fact = fact * n;
      n--;
    }

    //In that same line the factorial value is also print
    System.out.println(" Factorial is "+fact);
    //In every iteration n value decreases
    //System.out.println(n+" Factorial is "+fact);
  }
}

5 Factorial is 120

For the above while loop, we can also write the code as

public class Factorial {
  public static void main(String[] args) {
    int n= 6, fact=1, i=1;

    while(i<=n){
      fact = fact * i;
      i++;
    }
    System.out.println(n+" Factorial is "+fact);
  }
}

6 Factorial is 720

Factorial using recursion

Recursion is nothing but calling the function itself again and again.

public class Factorial {
  public static void main(String[] args) {
    int num = 4;
    System.out.println(num+" Factorial is "+fact(num));
  }

  public static int fact(int num){
    if(num==0)
      return 1;

    return num * fact(num-1);
  }
}

4 Factorial is 24

num = 4

4!

fact(4) = 4*fact(3) = 4*6 =24

fact(3) = 3 * fact(2) = 3*2 =6

fact(2) = 2 * fact(1) = 2*1 =2

fact(1) = 1 * fact(0) = 1*1 =1

Here n==0 return 1;

Finally, return the output to the main function call.