# Java Program for factorial of a number

Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. In this article, we will learn how to write a program for the factorial of a number in Java.

### Formulae for Factorial

`n! = n * (n-1) * (n-2) * (n-3) * ........ * 1`

### Example of Factorial in Java

6! == 6*5*4*3*2*1 = 720.
5! == 5*4*3*2*1 = 120
4! == 4*3*2*1 = 24

## Methods to Find Factorial of a Number

### 1. Iterative Solution for Factorial in Java

Below is the implementation of the above method:

## Java

 `// Java program to find factorial ``// of given number `` ` `// Driver Class ``class` `Test { ``    ``// Method to find factorial ``    ``// of given number ``    ``static` `int` `factorial(``int` `n) ``    ``{ ``        ``int` `res = ``1``, i; ``        ``for` `(i = ``2``; i <= n; i++) ``            ``res *= i; ``        ``return` `res; ``    ``} `` ` `    ``// main method ``    ``public` `static` `void` `main(String[] args) ``    ``{ ``        ``int` `num = ``5``; ``        ``System.out.println(``"Factorial of "` `+ num + ``" is "``                           ``+ factorial(``5``)); ``    ``} ``}`

Output
```Factorial of 5 is 120
```

#### The complexity of the above method:

Time Complexity: O(n)
Auxiliary Space: O(1)

### 2. Factorial in Java Using Recursive Method

Below is the implementation of the above method:

## Java

 `// Java program to find factorial ``// of given number `` ` `// Driver Class ``class` `Test { ``    ``// method to find factorial ``    ``// of given number ``    ``static` `int` `factorial(``int` `n) ``    ``{ ``        ``if` `(n == ``0``) ``            ``return` `1``; `` ` `        ``return` `n * factorial(n - ``1``); ``    ``} `` ` `    ``// main method ``    ``public` `static` `void` `main(String[] args) ``    ``{ ``        ``int` `num = ``5``; ``        ``System.out.println(``"Factorial of "` `+ num + ``" is "``                           ``+ factorial(``5``)); ``    ``} ``}`

Output
```Factorial of 5 is 120
```

#### The complexity of the above method:

Time Complexity: O(n)
Auxiliary Space: O(n)

### 3. One-line Solution (Using the Ternary operator)

Below is the implementation of the above method:

## Java

 `// Java program to find factorial ``// of given number `` ` `// Driver Class ``class` `Factorial { ``    ``// function to find factorial ``    ``int` `factorial(``int` `n) ``    ``{ `` ` `        ``// single line to find factorial ``        ``return` `(n == ``1` `|| n == ``0``) ? ``1``                                  ``: n * factorial(n - ``1``); ``    ``} `` ` `    ``// main function ``    ``public` `static` `void` `main(String args[]) ``    ``{ ``        ``Factorial obj = ``new` `Factorial(); ``        ``int` `num = ``5``; ``        ``System.out.println(``"Factorial of "` `+ num + ``" is "``                           ``+ obj.factorial(num)); ``    ``} ``}`

Output
```Factorial of 5 is 120
```

#### The complexity of the above method:

Time Complexity: O(n)
Auxiliary Space: O(n)

The above solutions cause overflow for small numbers. Please refer factorial of large numbers for a solution that works for large numbers. Please refer complete article on the Program for factorial of a number for more details!

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