# Program for factorial of a number

Factorial of a non-negative integer, is multiplication of all integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720. Recursive Solution:
Factorial can be calculated using following recursive formula.

```  n! = n * (n-1)!
n! = 1 if n = 0 or n = 1
```

Following is implementation of factorial.

## C++

 `// C++ program to find factorial of given number ` `#include ` `using` `namespace` `std; ` ` `  `// function to find factorial of given number ` `unsigned ``int` `factorial(unsigned ``int` `n) ` `{ ` `    ``if` `(n == 0) ` `    ``return` `1; ` `    ``return` `n * factorial(n - 1); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `num = 5; ` `    ``cout << ``"Factorial of "` `<< num << ``" is "` `<< factorial(num) << endl; ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by Shivi_Aggarwal `

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## C

 `// C program to find factorial of given number ` `#include ` ` `  `// function to find factorial of given number ` `unsigned ``int` `factorial(unsigned ``int` `n) ` `{ ` `    ``if` `(n == 0) ` `      ``return` `1; ` `    ``return` `n * factorial(n - 1); ` `} ` ` `  `int` `main() ` `{ ` `    ``int` `num = 5; ` `    ``printf``(``"Factorial of %d is %d"``, num, factorial(num)); ` `    ``return` `0; ` `} `

## Java

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

## Python3

 `# Python 3 program to find  ` `# factorial of given number ` `def` `factorial(n): ` `     `  `    ``# single line to find factorial ` `    ``return` `1` `if` `(n``=``=``1` `or` `n``=``=``0``) ``else` `n ``*` `factorial(n ``-` `1``);  ` ` `  `# Driver Code ` `num ``=` `5``; ` `print``(``"Factorial of"``,num,``"is"``, ` `factorial(num)) ` ` `  `# This code is contributed by Smitha Dinesh Semwal `

## C#

 `// C# program to find factorial ` `// of given number ` `using` `System; ` ` `  `class` `Test ` `{ ` `    ``// method to find factorial ` `    ``// of given number ` `    ``static` `int` `factorial(``int` `n) ` `    ``{ ` `        ``if` `(n == 0) ` `        ``return` `1; ` `         `  `        ``return` `n*factorial(n-1); ` `    ``} ` `     `  `    ``// Driver method ` `    ``public` `static` `void` `Main()  ` `    ``{ ` `        ``int` `num = 5; ` `        ``Console.WriteLine(``"Factorial of "` `          ``+ num + ``" is "` `+ factorial(5)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m `

## PHP

 ` `

Output:

`Factorial of 5 is 120`

Iterative Solution:
Factorial can also be calculated iteratively as recursion can be costly for large numbers.

## C++

 `// C++ program for factorial of a number ` `#include ` `using` `namespace` `std; ` ` `  `// function to find factorial of given number ` `unsigned ``int` `factorial(unsigned ``int` `n) ` `{ ` `    ``int` `res = 1, i; ` `    ``for` `(i = 2; i <= n; i++) ` `        ``res *= i; ` `    ``return` `res; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `num = 5; ` `    ``cout << ``"Factorial of "` `<< num << ``" is "` `<< factorial(num) << endl; ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by Shivi_Aggarwal `

## C

 `#include ` ` `  `// function to find factorial of given number ` `unsigned ``int` `factorial(unsigned ``int` `n) ` `{ ` `    ``int` `res = 1, i; ` `    ``for` `(i = 2; i <= n; i++) ` `        ``res *= i; ` `    ``return` `res; ` `} ` ` `  `int` `main() ` `{ ` `    ``int` `num = 5; ` `    ``printf``(``"Factorial of %d is %d"``, num, factorial(num)); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find factorial of given number ` `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; ` `    ``} ` `     `  `    ``// Driver method ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `num = ``5``; ` `        ``System.out.println(``"Factorial of "``+ num + ``" is "` `+ factorial(``5``)); ` `    ``} ` `} `

## Python3

 `# Python 3 program to find   ` `# factorial of given number ` `def` `factorial(n): ` `     `  `    ``# single line to find factorial ` `    ``return` `1` `if` `(n``=``=``1` `or` `n``=``=``0``) ``else` `n ``*` `factorial(n ``-` `1``);  ` ` `  `# Driver Code ` `num ``=` `5``; ` `print``(``"Factorial of"``,num,``"is"``, ` `factorial(num)) ` ` `  `# This code is contributed by Smitha Dinesh Semwal `

## C#

 `// C# program to find  ` `// factorial of given number ` `using` `System; ` ` `  `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; ` `    ``} ` `     `  `    ``// Driver method ` `    ``public` `static` `void` `Main()  ` `    ``{ ` `        ``int` `num = 5; ` `        ``Console.WriteLine(``"Factorial of "` `+ ` `               ``num + ``" is "` `+ factorial(5)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m `

## PHP

 ` `

Output :

`Factorial of 5 is 120`

Time complexity of the above solutions is O(n).

One line Solution (Using Ternary operator):

## C++

 `// C++ program to find factorial of given number ` `#include ` ` `  `int` `factorial(``int` `n) ` `{ ` `    ``// single line to find factorial ` `    ``return` `(n==1 || n==0) ? 1: n * factorial(n - 1);  ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `num = 5; ` `    ``printf` `(``"Factorial of %d is %d"``, num, factorial(num)); ` `    ``return` `0; ` `} ` ` `  `// This code is contributed by  Rithika palaniswamy. `

## Java

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

## Python3

 `# Python 3 program to find ` `# factorial of given number ` ` `  `def` `factorial(n): ` ` `  `    ``# single line to find factorial ` `    ``return` `1` `if` `(n``=``=``1` `or` `n``=``=``0``) ``else` `n ``*` `factorial(n ``-` `1``)  ` ` `  ` `  `# Driver Code ` `num ``=` `5` `print` `(``"Factorial of"``,num,``"is"``, ` `      ``factorial(num)) ` ` `  `# This code is contributed ` `# by Smitha Dinesh Semwal. `

## C#

 `// C# program to find factorial ` `// of given number ` `using` `System; ` ` `  `class` `Factorial { ` ` `  `    ``int` `factorial(``int` `n) ` `    ``{ ` `     `  `        ``// single line to find factorial ` `        ``return` `(n == 1 || n == 0) ? 1 : ` `                        ``n * factorial(n - 1); ` `     `  `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main()  ` `    ``{ ` `        ``Factorial obj = ``new` `Factorial(); ` `        ``int` `num = 5; ` `         `  `        ``Console.WriteLine(``"Factorial of "` `+ num +  ` `                        ``" is "` `+ obj.factorial(num)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` `

Output:

```Factorial of 5 is 120
```

The above solutions cause overflow for small numbers. Please refer factorial of large number for a solution that works for large numbers.

Please write comments if you find any bug in above code/algorithm, or find other ways to solve the same problem.