Euclidean algorithms (Basic and Extended)
The Euclidean algorithm is a way to find the greatest common divisor of two positive
integers. GCD of two numbers is the largest number that divides both of them. A simple
way to find GCD is to factorize both numbers and multiply common prime factors.
Basic Euclidean Algorithm for GCD:
The algorithm is based on the below facts.
If we subtract a smaller number from a larger one (we reduce a larger number), GCD
doesn’t change. So if we keep subtracting repeatedly the larger of two, we end up with
GCD.
Now instead of subtraction, if we divide the larger number, the algorithm stops when
we find the remainder 0.
Below is a recursive function to evaluate gcd using Euclid’s algorithm:
// Java program to demonstrate Basic Euclidean Algorithm
import java.lang.*;
import java.util.*;
class GFG {
// extended Euclidean Algorithm
public static int gcd(int a, int b)
{
if (a == 0)
return b;
return gcd(b % a, a);
}
