Program to find GCD or HCF of two numbers

1.3

GCD (Greatest Common Divisor) or HCF (Highest Common Factor) of two numbers is the largest number that divides both of them.

GCD

For example GCD of 20 and 28 is 4 and GCD of 98 and 56 is 14.

A simple solution is to find all prime factors of both numbers, then find intersection of all factors present in both numbers. Finally return product of elements in the intersection.

An efficient solution is to use Euclidean algorithm which is the main algorithm used for this purpose. The idea is, GCD of two numbers doesn’t change if smaller number is subtracted from a bigger number.

C

// C program to find GCD of two numbers
#include <stdio.h>

// Recursive function to return gcd of a and b
int gcd(int a, int b)
{
    // Everything divides 0 
    if (a == 0 || b == 0)
       return 0;

    // base case
    if (a == b)
        return a;

    // a is greater
    if (a > b)
        return gcd(a-b, b);
    return gcd(a, b-a);
}

// Driver program to test above function
int main()
{
    int a = 98, b = 56;
    printf("GCD of %d and %d is %d ", a, b, gcd(a, b));
    return 0;
}

Java

// Java program to find GCD of two numbers
class Test
{
    // Recursive function to return gcd of a and b
    static int gcd(int a, int b)
    {
        // Everything divides 0 
        if (a == 0 || b == 0)
           return 0;
     
        // base case
        if (a == b)
            return a;
     
        // a is greater
        if (a > b)
            return gcd(a-b, b);
        return gcd(a, b-a);
    }
    
    // Driver method
    public static void main(String[] args) 
    {
        int a = 98, b = 56;
        System.out.println("GCD of " + a +" and " + b + " is " + gcd(a, b));
    }
}


Output:
GCD of 98 and 56 is 14

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