Jul 22

Euclidean Algorithm

The Euclidean Algorithm recursively calculates the greatest common divisor (GCD) of two integers.  It works because GCD(a,b) = GCD(a mod b, b) = GCD(b, a mod b).  Each step of the algorithm reduces the size of the numbers by about a factor of 2.  The total number of steps required is roughly log(a*b).  It is much more efficient than brute force testing all possible divisors up to a+b.

#include <iostream>

int calcGCD(const int& a, const int& b)
    if (b == 0)
        return a;
    int aPrime = a % b;
    return calcGCD(b, aPrime);

int main()
    int aa, bb;
    std::cout << "Enter two integers for GCD: ";
    std::cin >> aa >> bb;
    std::cout << "Answer: " << calcGCD(aa, bb) << std::endl;

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