Java Program for Common Divisors of Two Numbers

Given two integer numbers, the task is to find the count of all common divisors of given numbers?

Input : a = 12, b = 24
Output: 6
// all common divisors are 1, 2, 3, 
// 4, 6 and 12

Input : a = 3, b = 17
Output: 1
// all common divisors are 1

Input : a = 20, b = 36
Output: 3
// all common divisors are 1, 2, 4

Java

// Java implementation of program

class Test {
    // method to calculate gcd of two numbers
    static int gcd(int a, int b)
    {
        if (a == 0)
            return b;

        return gcd(b % a, a);
    }
    // method to calculate all common divisors
    // of two given numbers
    // a, b --> input integer numbers
    static int commDiv(int a, int b)
    {
        // find gcd of a, b
        int n = gcd(a, b);

        // Count divisors of n.
        int result = 0;
        for (int i = 1; i <= Math.sqrt(n); i++) {
            // if 'i' is factor of n
            if (n % i == 0) {
                // check if divisors are equal
                if (n / i == i)
                    result += 1;
                else
                    result += 2;
            }
        }
        return result;
    }

    // Driver method
    public static void main(String args[])
    {
        int a = 12, b = 24;
        System.out.println(commDiv(a, b));
    }
}

Output:

6

Time complexity: O(sqrt(n)) because for loop will run for sqrt(n) times and function to calculate gcd will take O(log(min(a,b))

Auxiliary Space: O(log(min(a,b)) due to recursive stack space 

Please refer complete article on Common Divisors of Two Numbers for more details!