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C++ Program to Find GCD
The Greatest Common Divisor (GCD) of two numbers is the largest number that divides both of them.
For example: Let’s say we have two numbers are 45 and 27.
45 = 5 * 3 * 3 27 = 3 * 3 * 3
So, the GCD of 45 and 27 is 9.
A program to find the GCD of two numbers is given as follows.
Example
#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 = 105, b = 30;
cout<<"GCD of "<< a <<" and "<< b <<" is "<< gcd(a, b);
return 0;
}Output
GCD of 105 and 30 is 15
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 by the following code snippet −
int gcd(int a, int b) {
if (b == 0)
return a;
return gcd(b, a % b);
}Another program to find the GCD of two numbers is as follows −
Example
#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 = 105, b =30;
cout<<"GCD of "<< a <<" and "<< b <<" is "<< gcd(a, b);
return 0;
}Output
GCD of 105 and 30 is 15
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);
}
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