Question

Here is the question:

“Write a method named gcd that accepts two integers as parameters and returns the greatest common divisor of the two numbers. The greatest common divisor (GCD) of two integers a and b is the largest integer that is a factor of both a and b. The GCD of any number and 1 is 1, and the GCD of any number and 0 is that number.

One efficient way to compute the GCD of two numbers is to use Euclid’s algorithm, which states the following:

GCD(A, B) = GCD(B, A % B) 
GCD(A, 0) = Absolute value of A"

I’m really confused as to how to solve this problem. I just want some hints and tips as to what I did wrong in the program I have so far. (I have to put in a Scanner, that is my teacher’s requirement.)
Don’t give me a full code as I kinda want to solve this out myself. Maybe just give me a hint on how I incorporate this formula that you see above. (And if you’re wondering why I put in the == 0, it’s because I thought that if you have two numbers, say 0 and 90, their GCD would be 0 right??)

Also, my code has to include while loops…I would’ve preferred if loops…

Thanks in advance! 🙂

My current program:

public static void main(String[] args) {
        Scanner console = new Scanner(System.in);
        int a = console.nextInt();
        int b = console.nextInt();
        gcd (a, b);
    }

    public static void gcd(int a, int b) {
        System.out.print("Type in two numbers and I will print outs its Greatest Common Divisor: ");
        int gcdNum1 = console.nextInt();
        int gcdNum2 = console.nextInt();
        while (gcdNum1 == 0) {
            gcdNum1 = 0;
        }
        while (gcdNum2 > gcdNum1) {
            int gcd = gcdNum1 % gcdNum2;
        }
        System.out.print(gcdNum1 + gcdNum2);
    }
}

Answer 1

A recursive method would be:

static int gcd(int a, int b)
{
  if(a == 0 || b == 0) return a+b; // base case
  return gcd(b,a%b);
}

Using a while loop:

static int gcd(int a, int b)
{
  while(a!=0 && b!=0) // until either one of them is 0
  {
     int c = b;
     b = a%b;
     a = c;
  }
  return a+b; // either one is 0, so return the non-zero value
}

When I’m returning a+b, I’m actually returning the non-zero number assuming one of them is 0.