In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), or highest common factor (hcf), of two or more integers (at least one of which is not zero), is the largest positive integer that divides the numbers without a remainder – from Wikipedia

For example, the GCD of 8 and 12 is 4

Euclidian method: This is also called division algorithm. Take smallest of the two numbers and divide the other number. If the remainder is zero smaller number is the GCD. Otherwise replace the smaller number with remainder, and bigger number with present smaller number and repeat the same procedure.

For example, the GCD of 8 and 12 is 4

Euclidian method: This is also called division algorithm. Take smallest of the two numbers and divide the other number. If the remainder is zero smaller number is the GCD. Otherwise replace the smaller number with remainder, and bigger number with present smaller number and repeat the same procedure.

Here is the step-by-step calculation

8)12(1

8

—-

4)8(2

8

—

0

The following c++ code implements the iterative and recursive version of Euclidian algorithm.

#include <iostream>

using namespace std;

void swap(int &x, int &y)

{

int temp = x;

x = y;

y = temp;

}

//iterative version of Euclidian algorithm

int gcd(int x,int y)

{

while ( (y % x) != 0)

{

int r = y % x;

y = x;

x = r;

}

return x;

}

//recursive version of Euclidian algorithm

int gcd_recursive(int x, int y)

{

if( y % x == 0)

return x;

return gcd_recursive( y%x, x);

}

int main()

{

int x,y;

//read two numbers

cin>>x>>y;

//both iterative and recursive versions requires first parameter <= second

//swap if firt is greater

if( x > y )

{

swap(x,y);

}

cout<<"GCD(" << x << "," << y << ")=" << gcd_recursive(x,y) << endl;

return 0;

}