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Program to find HCF (Highest Common Factor) of 2 Numbers

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HCF (Highest Common Factor) or GCD (Greatest Common Divisor) 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 the intersection of all factors present in both numbers. Finally, return the 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


                    

Java


                    

Python3


                    

C#

// C# program to find GCD of two
// numbers
using System;
 
class GFG {
 
    // 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;
        if (a == 0)
            return b;
        if (b == 0)
            return a;
 
        // 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()
    {
        int a = 98, b = 56;
        Console.WriteLine("GCD of " + a + " and " + b
                          + " is " + gcd(a, b));
    }
}
 
// This code is contributed by anuj_67.

                    

Javascript

<script>
 
// Javascript program to find GCD of two numbers
 
// Recursive function to return gcd of a and b
function gcd(a, b)
{
     
    // Everything divides 0
    if (a == 0 && b == 0)
        return 0;
    if (a == 0)
        return b;
    if (b == 0)
        return a;
 
    // Base case
    if (a == b)
        return a;
 
    // a is greater
    if (a > b)
        return gcd(a - b, b);
         
    return gcd(a, b - a);
}
 
// Driver code
var a = 98, b = 56;
 
document.write("GCD of " + a + " and " +
                  b + " is " +  gcd(a, b));
                   
// This code is contributed by noob2000
 
</script>

                    

PHP


                    

Output
GCD of 0 and 56 is 56

Time Complexity: O(max(a,b)), where a and b are the given two integers.
Auxiliary Space: O(max(a,b)), where a and b are the given two integers.

A more efficient solution is to use modulo operator in Euclidean algorithm

C++


                    

C


                    

Java


                    

Python3


                    

C#

// C# program to find GCD of two
// numbers
using System;
 
class GFG {
     
    // Recursive function to return
    // gcd of a and b
    static int gcd(int a, int b)
    {     
       if (b == 0)
          return a;
       return gcd(b, a % b);
    }
     
    // Driver method
    public static void Main()
    {
        int a = 98, b = 56;
        Console.WriteLine("GCD of "
          + a +" and " + b + " is "
                      + gcd(a, b));
    }
}
 
// This code is contributed by anuj_67.

                    

Javascript


                    

PHP


                    

Output
GCD of 98 and 56 is 14

Time Complexity: O(log(max(a,b)), where a and b are the given two integers.
Auxiliary Space: O(log(max(a,b)), where a and b are the given two integers.

Please refer GCD of more than two (or array) numbers to find HCF of more than two numbers.
 



Last Updated : 07 Jan, 2024
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