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GCD of more than two (or array) numbers

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  • Difficulty Level : Easy
  • Last Updated : 21 Jun, 2022

Given an array of numbers, find GCD of the array elements. In a previous post we find GCD of two number.
Examples:
 

Input  : arr[] = {1, 2, 3}
Output : 1

Input  : arr[] = {2, 4, 6, 8}
Output : 2

The GCD of three or more numbers equals the product of the prime factors common to all the numbers, but it can also be calculated by repeatedly taking the GCDs of pairs of numbers. 
 

gcd(a, b, c) = gcd(a, gcd(b, c)) 
             = gcd(gcd(a, b), c) 
             = gcd(gcd(a, c), b)

For an array of elements, we do the following. We will also check for the result if the result at any step becomes 1 we will just return the 1 as gcd(1,x)=1. 
 

result = arr[0]
For i = 1 to n-1
   result = GCD(result, arr[i])

Complete Interview Preparation - GFG

Below is the implementation of the above idea.
 

C++




// C++ program to find GCD of two or
// more numbers
#include <bits/stdc++.h>
using namespace std;
  
// Function to return gcd of a and b
int gcd(int a, int b)
{
    if (a == 0)
        return b;
    return gcd(b % a, a);
}
  
// Function to find gcd of array of
// numbers
int findGCD(int arr[], int n)
{
    int result = arr[0];
    for (int i = 1; i < n; i++)
    {
        result = gcd(arr[i], result);
  
        if(result == 1)
        {
           return 1;
        }
    }
    return result;
}
  
// Driver code
int main()
{
    int arr[] = { 2, 4, 6, 8, 16 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << findGCD(arr, n) << endl;
    return 0;
}

Java




// Java program to find GCD of two or
// more numbers
  
public class GCD {
    // Function to return gcd of a and b
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }
  
    // Function to find gcd of array of
    // numbers
    static int findGCD(int arr[], int n)
    {
        int result = arr[0];
        for (int element: arr){
            result = gcd(result, element);
  
            if(result == 1)
            {
               return 1;
            }
        }
  
        return result;
    }
  
    public static void main(String[] args)
    {
        int arr[] = { 2, 4, 6, 8, 16 };
        int n = arr.length;
        System.out.println(findGCD(arr, n));
    }
}
  
// This code is contributed by Saket Kumar

Python




# GCD of more than two (or array) numbers
  
# Function implements the Euclidean 
# algorithm to find H.C.F. of two number
def find_gcd(x, y):
      
    while(y):
        x, y = y, x % y
      
    return x
          
# Driver Code        
l = [2, 4, 6, 8, 16]
  
num1 = l[0]
num2 = l[1]
gcd = find_gcd(num1, num2)
  
for i in range(2, len(l)):
    gcd = find_gcd(gcd, l[i])
      
print(gcd)
  
# Code contributed by Mohit Gupta_OMG

C#




// C# program to find GCD of 
// two or more numbers
using System;
  
public class GCD {
      
    // Function to return gcd of a and b
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }
  
    // Function to find gcd of 
    // array of numbers
    static int findGCD(int[] arr, int n)
    {
        int result = arr[0];
        for (int i = 1; i < n; i++){
            result = gcd(arr[i], result);
  
            if(result == 1)
            {
               return 1;
            }
        }
  
        return result;
    }
      
    // Driver Code
    public static void Main()
    {
        int[] arr = { 2, 4, 6, 8, 16 };
        int n = arr.Length;
        Console.Write(findGCD(arr, n));
    }
}
  
// This code is contributed by nitin mittal

PHP




<?php
// PHP program to find GCD of two or
// more numbers
  
// Function to return gcd of a and b
function gcd( $a, $b)
{
    if ($a == 0)
        return $b;
    return gcd($b % $a, $a);
}
  
// Function to find gcd of array of
// numbers
function findGCD($arr, $n)
{
    $result = $arr[0];
  
    for ($i = 1; $i < $n; $i++){
        $result = gcd($arr[$i], $result);
  
        if($result == 1)
        {
           return 1;
        }
    }
    return $result;
}
  
// Driver code
$arr = array( 2, 4, 6, 8, 16 );
$n = sizeof($arr);
echo (findGCD($arr, $n));
  
// This code is contributed by
// Prasad Kshirsagar.
?>

Javascript




<script>
  
// Javascript program to find GCD of two or 
// more numbers 
  
// Function to return gcd of a and b 
function gcd(a, b) 
    if (a == 0) 
        return b; 
    return gcd(b % a, a); 
  
// Function to find gcd of array of 
// numbers 
function findGCD(arr, n) 
    let result = arr[0]; 
    for (let i = 1; i < n; i++) 
    
        result = gcd(arr[i], result); 
  
        if(result == 1) 
        
        return 1; 
        
    
    return result; 
  
// Driver code 
  
    let arr = [ 2, 4, 6, 8, 16 ]; 
    let n = arr.length; 
    document.write(findGCD(arr, n) + "<br>"); 
  
// This is code is contributed by Mayank Tyagi
  
</script>

Output:  

2

Time Complexity: O(N * log(N)), where N is the largest element of the array
Auxiliary Space: O(1)

Recursive Method: Implementation of Algorithm recursively :

C++




#include <bits/stdc++.h>
using namespace std;
  
// recursive implementation
int GcdOfArray(vector<int>& arr, int idx)
{
    if (idx == arr.size() - 1) {
        return arr[idx];
    }
    int a = arr[idx];
    int b = GcdOfArray(arr, idx + 1);
    return __gcd(
        a, b); // __gcd(a,b) is inbuilt library function
}
  
int main()
{
    vector<int> arr = { 1, 2, 3 };
    cout << GcdOfArray(arr, 0) << "\n";
  
    arr = { 2, 4, 6, 8 };
    cout << GcdOfArray(arr, 0) << "\n";
    return 0;
}

Java




import java.util.*;
class GFG
{
    
    // Recursive function to return gcd of a and b  
    static int __gcd(int a, int b)  
    {  
        return b == 0? a:__gcd(b, a % b);     
    }
    
// recursive implementation
static int GcdOfArray(int[] arr, int idx)
{
    if (idx == arr.length - 1) {
        return arr[idx];
    }
    int a = arr[idx];
    int b = GcdOfArray(arr, idx + 1);
    return __gcd(
        a, b); // __gcd(a,b) is inbuilt library function
}
  
public static void main(String[] args)
{
   int[] arr = { 1, 2, 3 };
    System.out.print(GcdOfArray(arr, 0)+ "\n");
  
    int[] arr1 = { 2, 4, 6, 8 };
    System.out.print(GcdOfArray(arr1, 0)+ "\n");
}
}
  
// This code is contributed by gauravrajput1

Python3




# To find GCD of an array by recursive approach       
import math
  
# Recursive Implementation
def GcdOfArray(arr, idx):
    if idx == len(arr)-1:
        return arr[idx]
        
    a = arr[idx]
    b = GcdOfArray(arr,idx+1)
      
    return math.gcd(a, b)
  
# Driver Code 
arr = [1, 2, 3]
print(GcdOfArray(arr,0))
  
arr = [2, 4, 6, 8]
print(GcdOfArray(arr,0))
  
# Code contributed by Gautam goel (gautamgoel962)

C#




// To find GCD of an array by recursive approach
using System;
   
public class GCD {
       
    // Function to return gcd of a and b
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }
   
    // Recursive Implementation
    static int GcdOfArray(int[] arr, int idx)
    {
        if(idx==arr.Length-1)
        {
            return arr[idx];
        }
        int a = arr[idx];
        int b = GcdOfArray(arr, idx + 1);
        return gcd(a,b);
          
    }
       
    // Driver Code
    public static void Main()
    {
        int[] arr = { 1,2,3 };
        Console.Write(GcdOfArray(arr, 0)+"\n");
          
        int[] arr1 = { 2,4,6,8 };
        Console.Write(GcdOfArray(arr1, 0));
    }
}
   
// This code is contributed by adityapatil12

Javascript




// JavaScript code to implement this approach
  
// function to calculate gcd
function gcd(a, b) 
    if (!b) 
       return a;
    return gcd(b, a % b); 
}
  
// recursive implementation
function GcdOfArray(arr, idx)
{
    if (idx == arr.length - 1) {
        return arr[idx];
    }
    var a = arr[idx];
    var b = GcdOfArray(arr, idx + 1);
    return gcd(a, b); 
}
  
// Driver Code
var arr = [ 1, 2, 3 ];
console.log(GcdOfArray(arr, 0));
  
arr = [ 2, 4, 6, 8 ];
console.log(GcdOfArray(arr, 0));
  
// This code is contributed by phasing17

Output

1
2

Time Complexity: O(N * log(N)), where N is the largest element of the array

Auxiliary Space: O(N)

This article is contributed by DANISH_RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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