C++ Program to Find G.C.D Using Recursion

The Greatest Common Divisor (GCD) of two numbers is the largest number that divides both of them.

For example: Let’s say we have following two numbers: 45 and 27

63 = 7 * 3 * 3
42 = 7 * 3 * 2
So, the GCD of 63 and 42 is 21

A program to find the GCD of two numbers using recursion is given as follows.

Example

 Live Demo

#include<iostream>
using namespace std;
int gcd(int a, int b) {
   if (a == 0 || b == 0)
   return 0;
   else if (a == b)
   return a;
   else if (a > b)
   return gcd(a-b, b);
   else return gcd(a, b-a);
}
int main() {
   int a = 63, b = 42;
   cout<<"GCD of "<< a <<" and "<< b <<" is "<< gcd(a, b);
   return 0;
}

Output

GCD of 63 and 42 is 21

In the above program, gcd() is a recursive function. It has two parameters i.e. a and b. If a or b is 0, the function returns 0. If a or b are equal, the function returns a. If a is greater than b, the function recursively calls itself with the values a-b and b. If b is greater than a, the function recursively calls itself with the values a and b-a.

This is demonstrated by the following code snippet.

int gcd(int a, int b) {
   if (a == 0 || b == 0)
   return 0;
   else if (a == b)
   return a;
   else if (a > b)
   return gcd(a-b, b);
   else return gcd(a, b-a);
}

Another method of finding the GCD of two numbers using recursion is as follows.

Example

 Live Demo

#include <iostream>
using namespace std;
int gcd(int a, int b) {
   if (b == 0)
   return a;
   return gcd(b, a % b);
}
int main() {
   int a = 63, b = 42;
   cout<<"GCD of "<< a <<" and "<< b <<" is "<< gcd(a, b);
   return 0;
}

Output

GCD of 63 and 42 is 21

In the above program, gcd() is a recursive function. It has two parameters i.e. a and b. If b is greater than 0, then a is returned to the main() function. Otherwise, the gcd() function recursively calls itself with the values b and a%b.

This is demonstrated using the following code snippet.

int gcd(int a, int b) {
   if (b == 0)
   return a;
   return gcd(b, a % b);
}