# Program for factorial of a number

## What is the factorial of a number?

- Factorial of a non-negative integer is the multiplication of all positive integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720.
- A factorial is represented by a number and a ” ! ” mark at the end. It is widely used in permutations and combinations to calculate the total possible outcomes. A French mathematician Christian Kramp firstly used the exclamation.

**Recursive Solution to find factorial of a number:**

Let’s create a factorial program using recursive functions. Until the value is not equal to zero, the recursive function will call itself. Factorial can be calculated using the following recursive formula.

n! = n * (n – 1)!

n! = 1 if n = 0 or n = 1

Below is the implementation:

## C++

`// C++ program to find` `// factorial of given number` `#include <iostream>` `using` `namespace` `std;` `// Function to find factorial` `// of given number` `unsigned ` `int` `factorial(unsigned ` `int` `n)` `{` ` ` `if` `(n == 0 || n == 1)` ` ` `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` |

## C

`// C program to find factorial of given number` `#include <stdio.h>` `// 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` `# Function to find factorial of given number` `def` `factorial(n):` ` ` ` ` `if` `n ` `=` `=` `0` `:` ` ` `return` `1` ` ` ` ` `return` `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

`<?php` `// PHP program to find factorial` `// of given number` `// function to find factorial` `// of given number` `function` `factorial(` `$n` `)` `{` ` ` `if` `(` `$n` `== 0)` ` ` `return` `1;` ` ` `return` `$n` `* factorial(` `$n` `- 1);` `}` ` ` `// Driver Code` ` ` `$num` `= 5;` ` ` `echo` `"Factorial of "` `, ` `$num` `, ` `" is "` `, factorial(` `$num` `);` `// This code is contributed by m_kit` `?>` |

## Javascript

`<script>` `// Javascript to find factorial` `// of given number` `// function to find factorial` `// of given number` `function` `factorial(n) {` ` ` `if` `(n == 0) ` `return` `1;` ` ` `return` `n * factorial(n - 1);` `}` `// Driver Code` `let num = 5;` `document.write(` `"Factorial of "` `+ num + ` `" is "` `+ factorial(num));` `// This code is contributed by Saurabh Jaiswal` `</script>` |

**Output**

Factorial of 5 is 120

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

**Iterative Solution to find factorial of a number:**

Factorial can also be calculated iteratively as recursion can be costly for large numbers. Here we have shown the iterative approach using both for and while loops.

**Approach 1: **Using For loop

Follow the steps to solve the problem:

- Using a for loop, we will write a program for finding the factorial of a number.
- An integer variable with a value of 1 will be used in the program.
- With each iteration, the value will increase by 1 until it equals the value entered by the user.
- The factorial of the number entered by the user will be the final value in the fact variable.

Below is the implementation for the above approach:

## C++

`// C++ program for factorial of a number` `#include <iostream>` `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 <stdio.h>` `// 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 the 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` `# Function to find factorial of given number` `def` `factorial(n):` ` ` ` ` `res ` `=` `1` ` ` ` ` `for` `i ` `in` `range` `(` `2` `, n` `+` `1` `):` ` ` `res ` `*` `=` `i` ` ` `return` `res` `# 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

`<?php` `// function to find factorial` `// of given number` `function` `factorial( ` `$n` `)` `{` ` ` `$res` `= 1; ` `$i` `;` ` ` `for` `(` `$i` `= 2; ` `$i` `<= ` `$n` `; ` `$i` `++)` ` ` `$res` `*= ` `$i` `;` ` ` `return` `$res` `;` `}` `// Driver Code` `$num` `= 5;` `echo` `"Factorial of "` `, ` `$num` `, ` `" is "` `,` ` ` `factorial(` `$num` `);` `// This code is contributed` `// by anuj_67.` `?>` |

## Javascript

`<script>` `// JavaScript program to find factorial of given number` ` ` `// Method to find factorial of the given number` ` ` `function` `factorial(n)` ` ` `{` ` ` `var` `res = 1, i;` ` ` `for` `(i = 2; i <= n; i++)` ` ` `res *= i;` ` ` `return` `res;` ` ` `}` ` ` `// Driver method` ` ` ` ` `var` `num = 5;` ` ` `document.write(` `"Factorial of "` `+ num + ` `" is "` `+ factorial(5));` `// This code is contributed by shivanisinghss2110.` `</script>` |

**Output**

Factorial of 5 is 120

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

**Approach 2:** This example uses a while loop to implement the algorithm and find the factorial program.

## C

`// C program for factorial of a number` `#include <stdio.h>` `// function to find factorial of given number` `unsigned ` `int` `factorial(unsigned ` `int` `n)` `{` ` ` `if` `(n == 0)` ` ` `return` `1;` ` ` `int` `i = n, fact = 1;` ` ` `while` `(n / i != n) {` ` ` `fact = fact * i;` ` ` `i--;` ` ` `}` ` ` `return` `fact;` `}` `int` `main()` `{` ` ` `int` `num = 5;` ` ` `printf` `(` `"Factorial of %d is %d"` `, num, factorial(num));` ` ` `return` `0;` `}` |

## C++

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

## Java

`// Java program to find factorial of given number` `class` `Test {` ` ` `// Method to find factorial of the given number` ` ` `static` `int` `factorial(` `int` `n)` ` ` `{` ` ` `if` `(n == ` `0` `)` ` ` `return` `1` `;` ` ` `int` `i = n, fact = ` `1` `;` ` ` `while` `(n / i != n) {` ` ` `fact = fact * i;` ` ` `i--;` ` ` `}` ` ` `return` `fact;` ` ` `}` ` ` `// 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` `# Function to find factorial of given number` `def` `factorial(n):` ` ` `if` `(n ` `=` `=` `0` `):` ` ` `return` `1` ` ` `i ` `=` `n` ` ` `fact ` `=` `1` ` ` ` ` `while` `(n ` `/` `i !` `=` `n):` ` ` `fact ` `=` `fact ` `*` `i` ` ` `i ` `-` `=` `1` ` ` ` ` `return` `fact` `# 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;` ` ` `int` `i = n, fact = 1;` ` ` `while` `(n / i != n) {` ` ` `fact = fact * i;` ` ` `i--;` ` ` `}` ` ` `return` `fact;` ` ` `}` ` ` `// Driver method` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `num = 5;` ` ` `Console.WriteLine(` ` ` `"Factorial of "` `+ num` ` ` `+ ` `" is "` `+ factorial(5));` ` ` `}` `}` |

## Javascript

`<script>` ` ` `// JavaScript Program to implement` ` ` `// the above approach` ` ` `// function to find factorial of given` ` ` `// number using while loop` ` ` `function` `factorial(n) {` ` ` `if` `(n == 0)` ` ` `return` `1;` ` ` `let i = n, fact = 1;` ` ` `while` `(Math.floor(n / i) != n) {` ` ` `fact = fact * i;` ` ` `i--;` ` ` `}` ` ` `return` `fact;` ` ` `}` ` ` `// Driver code` ` ` `let num = 5;` ` ` `document.write(` `"Factorial of "` ` ` `+ num + ` `" is "` ` ` `+ factorial(num) + ` `"<br>"` `);` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output**

Factorial of 5 is 120

**Time complexity: **O(N)**Auxiliary Space: **O(1)

**Approach 3: **A ternary operator can be thought of as a shorthand for an if…else statement. The conditions are provided, along with statements to be executed based on them. Hereâ€™s the program for factorial using a ternary operator.

## C++

`// C++ program to find factorial of given number` `#include <iostream>` `using` `namespace` `std;` `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;` ` ` `cout << ` `"Factorial of "` `<< num << ` `" is "` `<< factorial(num);` ` ` `return` `0;` `}` `// This code is contributed by shivanisinghss2110` |

## C

`// C++ program to find factorial of given number` `#include <stdio.h>` `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 the 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

`<?php` `// PHP program to find factorial` `// of given number` `function` `factorial( ` `$n` `)` `{` ` ` ` ` `// single line to find factorial` ` ` `return` `(` `$n` `== 1 || ` `$n` `== 0) ? 1:` ` ` `$n` `* factorial(` `$n` `- 1);` `}` ` ` `// Driver Code` ` ` `$num` `= 5;` ` ` `echo` `"Factorial of "` `, ` `$num` `, ` `" is "` `, factorial(` `$num` `);` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// JavaScript program to find factorial of given number` `function` `factorial(n)` `{` ` ` `// single line to find factorial` ` ` `return` `(n == 1 || n == 0) ? 1 : n * factorial(n - 1);` `}` `// Driver Code` ` ` `var` `num = 5;` ` ` `document.write(` `"Factorial of "` `+num +` `" is "` `+ factorial(num));` `// This code is contributed by shivanisinghss2110.` `</script>` |

**Output**

Factorial of 5 is 120

**Time complexity: **O(n)**Auxiliary Space:** O(n)

## Problems in writing code of factorial

When the value of n changes increases by 1, the value of the factorial increases by n. So the variable storing the value of factorial should have a large size. Following is the value of n whose factorial can be stored in the respective size.

1. integer –> n<=12

2. long long int –> n<=19

From the above data, we can see that a very small value of n can be calculated because of the faster growth of the factorial function. We can however find the mod value of factorial of larger values by taking mod at each step.

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

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