How to write a Java function to implement Euclid's algorithm for computing the greatest common divisor gcd(m, n)

Question

I need to edit the main function to compute (m,n) for all m and n between 2 and 10, but I am not sure how to do so.

I need to write a Java function to implement Euclid's algorithm for computing the greatest common divisor gcd(m, n), which is the largest integer k dividing both m and n.

When the loop stops, the gcd is in m. Add the gcd() function to the NumericFunctions class and include code in main() to compute gcd(m, n) for all m and n between 2 and 10.

Source code:

public class NumericFunctions {

   public static long factorial(int n) {

      long result = 1;

      for (int i = 2; i <= n; i++) {

         result *= i;
      }
      return result;
   }

   public static int gcd (int n, int m) {

      if ((m % n) == 0) 

         return n;

      else

         return gcd(n, m % n);
}

     public static void main(String[] args) {

         for (int n = 1; n <= 10; n++)

            for (int m = 1; m <= 10; m++){

               System.out.println(gcd(n,m));

               System.out.println(" ");


            }
      }

Answer 1

There was an infinite recursion in your gcd() function (gcd(2, 1); for example). So, change your function for something like this

public static int gcd (int n, int m) {

    if (m > n) {
      if ((m % n) == 0) 
         return n;
      else
         return gcd(n, m % n);
    }
    else {
        if ((n % m) == 0) 
             return m;
          else
             return gcd(m, n % m);
    }
}

public static void main(String[] args) {    

    for (int n = 1; n <= 10; n++) {

        for (int m = 1; m <= 10; m++) {
            System.out.println("n: " + n + " m: " + m + " gcd: " + gcd(n, m));
        }
    }
}