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Find an array element such that all elements are divisible by it

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Given an array of numbers, find the number among them such that all numbers are divisible by it. If not possible print -1.

Examples: 

Input : arr = {25, 20, 5, 10, 100} 
Output : 5 
Explanation : 5 is an array element
 which divides all numbers.

Input : arr = {9, 3, 6, 2, 15} 
Output : -1 
Explanation : No numbers are divisible
by any array element.

Method 1:(naive): A normal approach will be to take every element and check for division with all other elements. If all the numbers are divisible then return the number. 

Implementation:

C++

// CPP program to find an array element that 
// divides all numbers in the array using
// naive approach
#include <bits/stdc++.h>
using namespace std;
  
// function to find smallest num
int findSmallest(int a[], int n)
{
    // traverse for all elements
    for (int i = 0; i < n; i++) {
          
        int j;
        for (j = 0; j < n; j++) 
            if (a[j] % a[i]) 
                break;
  
        // stores the minimum if
        // it divides all
        if (j == n)
            return a[i];
    }
  
    return -1;
}
  
// driver code
int main()
{
    int a[] = { 25, 20, 5, 10, 100 };
    int n = sizeof(a) / sizeof(int);
    cout << findSmallest(a, n);
    return 0;
}

                    

Java

// Java program to find an array element
// that divides all numbers in the array 
// using naive approach
import java.io.*;
  
class GFG {
      
    // function to find smallest num
    static int findSmallest(int a[], int n)
    {
        // traverse for all elements
        for (int i = 0; i < n; i++) 
        {
              
            int j;
            for (j = 0; j < n; j++) 
                if (a[j] % a[i]>=1
                    break;
      
            // stores the minimum if
            // it divides all
            if (j == n)
                return a[i];
        }
      
        return -1;
    }
      
    // driver code
    public static void main(String args[])
    {
        int a[] = { 25, 20, 5, 10, 100 };
        int n = a.length;
        System.out.println(findSmallest(a, n));
    }
}
  
  
// This code is contributed by Nikita Tiwari.

                    

Python3

# Python 3 program to find an array
# element that divides all numbers
# in the array using naive approach
  
# Function to find smallest num
def findSmallest(a, n) :
      
    # Traverse for all elements
    for i in range(0, n ) :
          
        for j in range(0, n) :
              
            if ((a[j] % a[i]) >= 1) :
                break
  
        # Stores the minimum 
        # if it divides all
        if (j == n - 1) :
            return a[i]
                  
    return -1
  
  
# Driver code
a = [ 25, 20, 5, 10, 100 ]
n = len(a)
print(findSmallest(a, n))
  
  
# This code is contributed by Nikita Tiwari.

                    

C#

// C# program to find an array element
// that divides all numbers in the array 
// using naive approach
using System;
  
class GFG {
      
    // function to find smallest num
    static int findSmallest(int []a, int n)
    {
        // traverse for all elements
        for (int i = 0; i < n; i++) 
        {
              
            int j;
            for (j = 0; j < n; j++) 
                if (a[j] % a[i] >= 1) 
                    break;
      
            // stores the minimum if
            // it divides all
            if (j == n)
                return a[i];
        }
      
        return -1;
    }
      
    // Driver code
    public static void Main()
    {
        int []a = { 25, 20, 5, 10, 100 };
        int n = a.Length;
        Console.WriteLine(findSmallest(a, n));
    }
}
  
  
// This code is contributed by vt_m.

                    

PHP

<?php
// PHP program to find an array 
// element that divides all 
// numbers in the array using
// naive approach
  
// function to find smallest num
function findSmallest($a, $n)
{
      
    // traverse for all elements
    for ($i = 0; $i < $n; $i++) 
    {
        $j;
        for ($j = 0; $j < $n; $j++) 
            if ($a[$j] % $a[$i]) 
                break;
  
        // stores the minimum if
        // it divides all
        if ($j == $n)
            return $a[$i];
    }
  
    return -1;
}
  
    // Driver Code
    $a = array( 25, 20, 5, 10, 100 );
    $n = sizeof($a);
    echo findSmallest($a, $n);
  
// This code is contributed by nitin mittal
?>

                    

Javascript

<script>
  
// JavaScript program to find an array element
// that divides all numbers in the array 
// using naive approach
  
    // function to find smallest num
    function findSmallest(a, n)
    {
        // traverse for all elements
        for (let i = 0; i < n; i++) 
        {
                
            let j;
            for (j = 0; j < n; j++) 
                if (a[j] % a[i]>=1) 
                    break;
        
            // stores the minimum if
            // it divides all
            if (j == n)
                return a[i];
        }
        
        return -1;
    }
   
// Driver code
  
        let a = [ 25, 20, 5, 10, 100 ];
        let n = a.length;
        document.write(findSmallest(a, n));
  
</script>

                    

Output
5

Time Complexity: O(n2)
Auxiliary Space: O(1)

Method 2 : (Efficient): An efficient approach is to find smallest of all numbers, and check if it divides all the other numbers, if yes then the smallest number will be the required number. 

Implementation:

C++

// CPP Program to find the smallest number
// that divides all numbers in an array
#include <bits/stdc++.h>
using namespace std;
  
// function to find smallest num
int findSmallest(int a[], int n)
    // Find the smallest element
    int smallest = *min_element(a, a+n);
      
    // Check if all array elements
    // are divisible by smallest.
    for (int i = 1; i < n; i++)     
        if (a[i] % smallest) 
            return -1;
  
    return smallest;
}
  
// Driver code
int main()
{
    int a[] = { 25, 20, 5, 10, 100 };
    int n = sizeof(a) / sizeof(int);    
    cout << findSmallest(a, n);    
    return 0;
}

                    

Java

// Java Program to find the 
// smallest number that divides
// all numbers in an array
import java.io.*;
  
class GFG {
  
    // function to find the smallest element
    static int min_element(int a[])
    {
        int min = Integer.MAX_VALUE, i;
        for (i = 0; i < a.length; i++) 
        {
            if (a[i] < min)
                min = a[i];
        }
          
        return min;
    }
      
    // function to find smallest num
    static int findSmallest(int a[], int n) 
    {
        // Find the smallest element
        int smallest = min_element(a);
      
        // Check if all array elements
        // are divisible by smallest.
        for (int i = 1; i < n; i++)
        if (a[i] % smallest >= 1)
            return -1;
      
        return smallest;
    }
      
    // Driver code
    public static void main(String args[])
    {
        int a[] = {25, 20, 5, 10, 100};
        int n = a.length;
        System.out.println(findSmallest(a, n));
    }
}
  
// This code is contributed by Nikita Tiwari.

                    

Python3

# Python3 Program to find the
# smallest number that divides
# all numbers in an array
  
# Function to find the smallest element
def min_element(a) :
      
    m = 10000000
      
    for i in range(0, len(a)) :
          
        if (a[i] < m) :
            m = a[i]
      
    return m
  
# Function to find smallest num
def findSmallest(a, n) :
      
    # Find the smallest element
    smallest = min_element(a)
      
    # Check if all array elements
    # are divisible by smallest.
    for i in range(1, n) :
          
        if (a[i] % smallest >= 1) :
            return -1
  
    return smallest
  
  
# Driver code
  
a = [ 25, 20, 5, 10, 100 ]
n = len(a)
print(findSmallest(a, n))
  
  
# This code is contributed by Nikita Tiwari.

                    

C#

// C# Program to find the 
// smallest number that divides
// all numbers in an array
using System;
  
class GFG {
  
    // function to find the smallest element
    static int min_element(int []a)
    {
        int min = int.MaxValue;
        int i;
        for (i = 0; i < a.Length; i++) 
        {
            if (a[i] < min)
                min = a[i];
        }
          
        return min;
    }
      
    // function to find smallest num
    static int findSmallest(int []a, int n) 
    {
        // Find the smallest element
        int smallest = min_element(a);
      
        // Check if all array elements
        // are divisible by smallest.
        for (int i = 1; i < n; i++)
        if (a[i] % smallest >= 1)
            return -1;
      
        return smallest;
    }
      
    // Driver code
    public static void Main()
    {
        int []a = {25, 20, 5, 10, 100};
        int n = a.Length;
        Console.WriteLine(findSmallest(a, n));
    }
}
  
// This code is contributed by vt_m.

                    

PHP

<?php
// PHP Program to find the smallest number
// that divides all numbers in an array
  
// function to find smallest num
function findSmallest($a, $n)
{
      
    // Find the smallest element
    $smallest = min($a);
      
    // Check if all array elements
    // are divisible by smallest.
    for ($i = 1; $i < $n; $i++) 
        if ($a[$i] % $smallest
            return -1;
  
    return $smallest;
}
  
    // Driver Code
    $a = array(25, 20, 5, 10, 100);
    $n =count($a);
    echo findSmallest($a, $n); 
  
// This code is contributed by anuj_67.
?>

                    

Javascript

<script>
    // Javascript Program to find the
    // smallest number that divides
    // all numbers in an array
      
    // function to find the smallest element
    function min_element(a)
    {
        let min = Number.MAX_VALUE;
        let i;
        for (i = 0; i < a.length; i++)
        {
            if (a[i] < min)
                min = a[i];
        }
           
        return min;
    }
       
    // function to find smallest num
    function findSmallest(a, n)
    {
        // Find the smallest element
        let smallest = min_element(a);
       
        // Check if all array elements
        // are divisible by smallest.
        for (let i = 1; i < n; i++)
        if (a[i] % smallest >= 1)
            return -1;
       
        return smallest;
    }
      
    let a = [25, 20, 5, 10, 100];
    let n = a.length;
    document.write(findSmallest(a, n));
      
    // This code is contributed by divyeshrabadiya07.
</script>

                    

Output
5

Time Complexity: O(n) 
Auxiliary Space: O(1)



Last Updated : 19 Sep, 2023
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