# Find Factorial of a given Number

Objective: Given a number, write a program to find factorial of that number.

What is Factorial Number?

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. The value of 0! is 1, according to the convention for an empty product

N! = n*(n-1)*(n-2)*…..*2*1

Example:

```5! = 5 x 4 x 3 x 2x 1 = 120
7! = 7 x 6 x 5 x 4 x 3 x 2x 1 = 5040
```

Approach:

Recursive Solution

• If number is 0, return 1.
• Make a recursive call to get the result of number – 1.
• Multiply number with the result of number – 1.

Java Code:

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 public class FactorialRecursion { public static int factorial(int num){ if(num==0) return 1; return num * factorial(num–1); } public static void main(String[] args) { int num = 10; int fact = factorial(num); System.out.println("Factorial of a number: " + num + " is(Recursion): " + fact); } }

Output:

`Factorial of a number: 10 is(Recursion): 3628800`

Iterative Solution:

• If number is 0, return 1.
• Run a loop from 2 to number and multiple all of them to get the result.

Java Code:

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`Factorial of a number: 7 is(Iterative): 5040`