Largest number dividing maximum number of elements in the array
Last Updated :
19 Aug, 2021
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 straightforward 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 straightforward 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++
#include <bits/stdc++.h>
using namespace std;
int findLargest( int * arr, int n)
{
int gcd = 0;
for ( int i = 0; i < n; i++)
gcd = __gcd(arr[i], gcd);
return gcd;
}
int main()
{
int arr[] = { 3, 6, 9 };
int n = sizeof (arr) / sizeof ( int );
cout << findLargest(arr, n);
return 0;
}
|
Java
class GFG {
static int findLargest( int [] arr, int n)
{
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);
}
public static void main(String[] args)
{
int arr[] = { 3 , 6 , 9 };
int n = arr.length;
System.out.print(findLargest(arr, n));
}
}
|
Python3
from math import gcd as __gcd
def findLargest(arr, n):
gcd = 0
for i in range (n):
gcd = __gcd(arr[i], gcd)
return gcd
if __name__ = = '__main__' :
arr = [ 3 , 6 , 9 ]
n = len (arr)
print (findLargest(arr, n))
|
C#
using System;
class GFG {
static int findLargest( int [] arr, int n)
{
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);
}
public static void Main(String[] args)
{
int [] arr = { 3, 6, 9 };
int n = arr.Length;
Console.Write(findLargest(arr, n));
}
}
|
Javascript
<script>
function findLargest(arr , n) {
var gcd = 0;
for (i = 0; i < n; i++)
gcd = __gcd(arr[i], gcd);
return gcd;
}
function __gcd(a , b) {
return b == 0 ? a : __gcd(b, a % b);
}
var arr = [ 3, 6, 9 ];
var n = arr.length;
document.write(findLargest(arr, n));
</script>
|
Time Complexity: O(N * log(MAX)), where N is the size of the array and MAX is the maximum element of the array.
Auxiliary Space: O(log(MAX))
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