Largest number dividing maximum number of elements in the array

Given an array arr[] of length N, the task is to find the largest number dividing the maximum number of elements from the array.

Examples:

Input: arr[] = {2, 12, 6}
Output: 2
1 and 2 are the only integers which divide the
maximum number of elements from the array
(i.e. all the elements) and 2 is
the maximum among them.



Input: arr[] = {1, 7, 9}
Output: 1

Approach: A straight forward approach for solving this problem will be taking the GCD of all the elements. Why this approach works? 1 is the number that divides all the elements of the array. Now, any other number greater than 1 will either divide all the elements of the array (in this case, the number itself is the answer) or it will divide a subset of the array i.e. 1 is the answer here as it divides more elements from the array. So, the most straight forward way for doing this will be to take the GCD of all the elements of the array.

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the largest number
// that divides the maximum elements
// fom the given array
int findLargest(int* arr, int n)
{
  
    // Finding gcd of all the numbers
    // in the array
    int gcd = 0;
    for (int i = 0; i < n; i++)
        gcd = __gcd(arr[i], gcd);
    return gcd;
}
  
// Driver code
int main()
{
    int arr[] = { 3, 6, 9 };
    int n = sizeof(arr) / sizeof(int);
  
    cout << findLargest(arr, n);
  
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implementation of the approach
class GFG
{
  
// Function to return the largest number
// that divides the maximum elements
// fom the given array
static int findLargest(int[] arr, int n)
{
  
    // Finding gcd of all the numbers
    // in the array
    int gcd = 0;
    for (int i = 0; i < n; i++)
        gcd = __gcd(arr[i], gcd);
    return gcd;
}
  
static int __gcd(int a, int b) 
    return b == 0 ? a : __gcd(b, a % b);     
}
  
// Driver code
public static void main(String[] args)
{
    int arr[] = { 3, 6, 9 };
    int n = arr.length;
  
    System.out.print(findLargest(arr, n));
}
}
  
// This code is contributed by PrinciRaj1992

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 implementation of the approach
from math import gcd as __gcd
  
# Function to return the largest number
# that divides the maximum elements
# fom the given array
def findLargest(arr, n):
  
    # Finding gcd of all the numbers
    # in the array
    gcd = 0
    for i in range(n):
        gcd = __gcd(arr[i], gcd)
    return gcd
  
# Driver code
if __name__ == '__main__':
    arr = [3, 6, 9]
    n = len(arr)
  
    print(findLargest(arr, n))
  
# This code is contributed by Mohit Kumar

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implementation of the approach
using System;
  
class GFG
{
  
// Function to return the largest number
// that divides the maximum elements
// fom the given array
static int findLargest(int[] arr, int n)
{
  
    // Finding gcd of all the numbers
    // in the array
    int gcd = 0;
    for (int i = 0; i < n; i++)
        gcd = __gcd(arr[i], gcd);
    return gcd;
}
  
static int __gcd(int a, int b) 
    return b == 0 ? a : __gcd(b, a % b);     
}
  
// Driver code
public static void Main(String[] args)
{
    int []arr = { 3, 6, 9 };
    int n = arr.Length;
  
    Console.Write(findLargest(arr, n));
}
}
  
// This code is contributed by PrinciRaj1992

chevron_right


Output:

3

GeeksforGeeks has prepared a complete interview preparation course with premium videos, theory, practice problems, TA support and many more features. Please refer Placement 100 for details




My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.