查找给定数组的元素阶乘的GCD

给定一个具有N个正整数的数组。找到数组所有元素的阶乘的GCD。
例子：

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

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

方法：要找到所有元素的阶乘的GCD，首先计算所有元素的阶乘，然后找出它们的GCD。但这似乎是一个漫长的过程。两个数字的GCD是将两个数字相除的最大数字。因此，两个数阶乘的GCD是最小数阶乘数本身的值。
例如：GCD为3！ (6)和5！ (120)是3！ (即6)本身。
因此，要找到给定数组所有元素的阶乘的GCD，找到最小的元素，然后打印其阶乘，这将是我们所需的答案。
下面是上述方法的实现：

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

 
// JavaScript implementation of the above approach   
 
// Implementation of factorial function
    function factorial(n) {
        return (n == 1 || n == 0) ? 1 : factorial(n - 1) * n;
    }
 
    // Function to find GCD of factorial of
    // elements from array
    function gcdOfFactorial(arr , n) {
        // find the minimum element of array
        var minm = arr[0];
        for (i = 1; i < n; i++)
            minm = minm > arr[i] ? arr[i] : minm;
 
        // return the factorial of minimum element
        return factorial(minm);
    }
 
    // Driver Code
     
        var arr = [ 9, 12, 122, 34, 15 ];
        var n = arr.length;
        document.write(gcdOfFactorial(arr, n));
 
// This code is contributed by todaysgaurav
 

输出：

362880