Count of integers that divide all the elements of the given array

Given an array arr[] of N elements. The task is to find the count of positive integers that divide all the array elements.

Examples:

Input: arr[] = {2, 8, 10, 6} 
Output: 2 
1 and 2 are the only integers that divide 
all the elements of the given array.

Input: arr[] = {6, 12, 18, 12, 6} 
Output: 4 

Approach: We know that the maximum integer that will divide all the array elements will be the gcd of the array and all the other integers that will divide all the elements of the array will have to be the factors of this gcd. Hence, the count of valid integers will be equal to the count of factors of the gcd of all the array elements.

Below is the implementation of the above approach: 

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to return the count of
// the required integers
int getCount(int a[], int n)
{

    // To store the gcd of the array elements
    int gcd = 0;
    for (int i = 0; i < n; i++)
        gcd = __gcd(gcd, a[i]);

    // To store the count of factors
    // of the found gcd
    int cnt = 0;

    for (int i = 1; i * i <= gcd; i++) {
        if (gcd % i == 0) {

            // If g is a perfect square
            if (i * i == gcd)
                cnt++;

            // Factors appear in pairs
            else
                cnt += 2;
        }
    }

    return cnt;
}

// Driver code
int main()
{
    int a[] = { 4, 16, 1024, 48 };
    int n = sizeof(a) / sizeof(a[0]);

    cout << getCount(a, n);

    return 0;
}

Java

// Java implementation of the approach
class GFG
{

    // Recursive function to return gcd
    static int calgcd(int a, int b)
    {
        if (b == 0)
            return a;
        return calgcd(b, a % b);
    }

    // Function to return the count of
    // the required integers
    static int getCount(int [] a, int n)
    {

        // To store the gcd of the array elements
        int gcd = 0;
        for (int i = 0; i < n; i++)
            gcd = calgcd(gcd, a[i]);

        // To store the count of factors
        // of the found gcd
        int cnt = 0;

        for (int i = 1; i * i <= gcd; i++)
        {
            if (gcd % i == 0)
            {

                // If g is a perfect square
                if (i * i == gcd)
                    cnt++;

                // Factors appear in pairs
                else
                    cnt += 2;
            }
        }
        return cnt;
    }

    // Driver code
    public static void main (String[] args)
    {
        int [] a = { 4, 16, 1024, 48 };
        int n = a.length;

        System.out.println(getCount(a, n));
    }
}

// This code is contributed by ihritik

Python3

# Python3 implementation of the approach

# Function to return the count of
# the required integers
from math import gcd as __gcd
def getCount(a, n):

    # To store the gcd of the array elements
    gcd = 0
    for i in range(n):
        gcd = __gcd(gcd, a[i])

    # To store the count of factors
    # of the found gcd
    cnt = 0

    for i in range(1, gcd + 1):
        if i * i > gcd:
            break
        if (gcd % i == 0):

            # If g is a perfect square
            if (i * i == gcd):
                cnt += 1

            # Factors appear in pairs
            else:
                cnt += 2

    return cnt

# Driver code
a = [4, 16, 1024, 48]
n = len(a)

print(getCount(a, n))

# This code is contributed by Mohit Kumar

C#

// C# implementation of the approach
using System;

class GFG
{

    // Recursive function to return gcd
    static int calgcd(int a, int b)
    {
        if (b == 0)
            return a;
        return calgcd(b, a % b);
    }

    // Function to return the count of
    // the required integers
    static int getCount(int [] a, int n)
    {

        // To store the gcd of the array elements
        int gcd = 0;
        for (int i = 0; i < n; i++)
            gcd = calgcd(gcd, a[i]);

        // To store the count of factors
        // of the found gcd
        int cnt = 0;

        for (int i = 1; i * i <= gcd; i++)
        {
            if (gcd % i == 0)
            {

                // If g is a perfect square
                if (i * i == gcd)
                    cnt++;

                // Factors appear in pairs
                else
                    cnt += 2;
            }
        }
        return cnt;
    }

    // Driver code
    public static void Main ()
    {
        int [] a = { 4, 16, 1024, 48 };
        int n = a.Length;

        Console.WriteLine(getCount(a, n));
    }
}

// This code is contributed by ihritik

Javascript

<script>

// Javascript implementation of the approach

function calgcd(a, b)
{
    if (b == 0)
        return a;
    return calgcd(b, a % b);
}

// Function to return the count of
// the required integers
function getCount(a, n)
{

    // To store the gcd of the array elements
    let gcd = 0;
    for (let i = 0; i < n; i++)
        gcd = calgcd(gcd, a[i]);

    // To store the count of factors
    // of the found gcd
    let cnt = 0;

    for (let i = 1; i * i <= gcd; i++) {
        if (gcd % i == 0) {

            // If g is a perfect square
            if (i * i == gcd)
                cnt++;

            // Factors appear in pairs
            else
                cnt += 2;
        }
    }

    return cnt;
}

// Driver code
    let a = [ 4, 16, 1024, 48 ];
    let n = a.length;

    document.write(getCount(a, n));

</script>

Output:

3

Time Complexity: O(N*log(max_element))
Auxiliary Space: O(1)