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 very lengthy process. GCD of two numbers is the greatest number which divides both of the numbers. Hence, GCD of factorial of two number is the value of factorial of 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 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++

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// C++ implementation of the above approach
  
#include <bits/stdc++.h>
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;
}

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Java

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// 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

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Python3

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# 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

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[/sourcecode]

C#

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// 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

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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
?>

Output:

362880


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