# Find GCD of factorial of elements of given array

Given an array with N positive integers. Find the GCD of factorials of all elements of array.
Examples:

```Input : arr[] = {3, 4, 8, 6}
Output : 6

Input : arr[] = {13, 24, 8, 5}
Output : 120```

Approach: To find the GCD of factorial of all elements, first of all, calculate the factorial of all elements and then find out their GCD. But this seems to be a very lengthy process. GCD of two numbers is the greatest number that divides both of the numbers. Hence, GCD of the factorial of two numbers is the value of the factorial of the smallest number itself.
For example, GCD of 3! (6) and 5! (120) is 3! (i.e. 6) itself.
Hence to find the GCD of factorial of all elements of the given array, find the smallest element and then print its factorial that will be our required answer.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach` `#include ``using` `namespace` `std;` `// Implementation of factorial function``int` `factorial(``int` `n)``{``    ``return` `(n == 1 || n == 0) ? 1 : factorial(n - 1) * n;``}` `// Function to find GCD of factorial of ``// elements from array``int` `gcdOfFactorial(``int` `arr[], ``int` `n)``{``    ``// find the minimum element of array``    ``int` `minm = arr[0];``    ``for` `(``int` `i = 1; i < n; i++)``        ``minm = minm > arr[i] ? arr[i] : minm;` `    ``// return the factorial of minimum element``    ``return` `factorial(minm);``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 9, 12, 122, 34, 15 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``cout << gcdOfFactorial(arr, n);``    ``return` `0;``}`

## Java

 `// Java implementation of the above approach``class` `GFG``{``    ` `// Implementation of factorial function``static` `int` `factorial(``int` `n)``{``    ``return` `(n == ``1` `|| n == ``0``) ? ``1` `: factorial(n - ``1``) * n;``}` `// Function to find GCD of factorial of ``// elements from array``static` `int` `gcdOfFactorial(``int` `[]arr, ``int` `n)``{``    ``// find the minimum element of array``    ``int` `minm = arr[``0``];``    ``for` `(``int` `i = ``1``; i < n; i++)``        ``minm = minm > arr[i] ? arr[i] : minm;` `    ``// return the factorial of minimum element``    ``return` `factorial(minm);``}` `// Driver Code``public` `static` `void` `main (String[] args) ``{``    ``int` `[]arr = { ``9``, ``12``, ``122``, ``34``, ``15` `};``    ``int` `n = arr.length;``    ``System.out.println(gcdOfFactorial(arr, n));``}``}` `// This code is contributed by mits`

## Python3

 `# Implementation of factorial function``def` `factorial(n):``    ``if` `n ``=``=` `1` `or` `n ``=``=` `0``:``        ``return` `1``    ``else``:``        ``return` `factorial(n ``-` `1``) ``*` `n` `# Function to find GCD of factorial ``# of elements from array``def` `gcdOfFactorial(arr, n):` `    ``# find the minimum element ``    ``# of array``    ``minm ``=` `arr[``0``]``    ``for` `i ``in` `range``(``1``, n):``        ``if` `minm > arr[i]:``            ``minm ``=` `arr[i]``        ``else``:``            ``arr[i] ``=` `minm` `    ``# return the factorial of ``    ``# minimum element``    ``return` `factorial(minm)` `# Driver Code``arr ``=` `[``9``, ``12``, ``122``, ``34``, ``15` `]``n ``=` `len``(arr)``print``(gcdOfFactorial(arr, n))` `# This code is contributed ``# by mohit kumar`

## C#

 `// C# implementation of the above approach``using` `System;` `class` `GFG``{``    ` `// Implementation of factorial function``static` `int` `factorial(``int` `n)``{``    ``return` `(n == 1 || n == 0) ? 1 : factorial(n - 1) * n;``}` `// Function to find GCD of factorial of ``// elements from array``static` `int` `gcdOfFactorial(``int` `[]arr, ``int` `n)``{``    ``// find the minimum element of array``    ``int` `minm = arr[0];``    ``for` `(``int` `i = 1; i < n; i++)``        ``minm = minm > arr[i] ? arr[i] : minm;` `    ``// return the factorial of minimum element``    ``return` `factorial(minm);``}` `// Driver Code``static` `void` `Main()``{``    ``int` `[]arr = { 9, 12, 122, 34, 15 };``    ``int` `n = arr.Length;``    ``Console.WriteLine(gcdOfFactorial(arr, n));``}``}` `// This code is contributed by mits`

## PHP

 ` ``\$arr``[``\$i``] ? ``                        ``\$arr``[``\$i``] : ``\$minm``; ` `    ``// return the factorial of minimum element ``    ``return` `factorial(``\$minm``); ``} ` `// Driver Code ``\$arr` `= ``array``( 9, 12, 122, 34, 15 ); ``\$n` `= ``count``(``\$arr``); ``echo` `gcdOfFactorial(``\$arr``, ``\$n``);` `// This code is contributed by Srathore``?>`

## Javascript

 ``

Output:
`362880`

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

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