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Print the kth common factor of two numbers

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  • Difficulty Level : Basic
  • Last Updated : 22 Jun, 2022
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Given three numbers x, y and k, find the k’th common factor of x and y. Print -1 if there are less than k common factors of x and y. 
Examples : 
 

Input : x = 20, y = 24
        k = 3
Output : 4
Common factors are 1, 2, 4, ...

Input : x = 4, y = 24
        k = 2
Output : 2

Input : x = 22, y = 2
        k = 3
Output : -1

 

We find the smaller of two numbers as common factor cannot be greater than the smaller number. Then we run a loop from 1 to the smaller number. For every number i, we check if it is a common factor. If yes, we increment count of common factors. 
Below is the Implementation : 
 

C++




// C++ program to find kth common factor
// of two numbers
#include<iostream>
using namespace std;
 
// Returns k'th common factor of x and y.
int findKCF(int x, int y, int k)
{
   // Find smaller of two numbers
   int small = min(x, y);
 
   // Count common factors until we either
   // reach small or count becomes k.
   int count = 1;
   for (int i=2; i<=small; i++)
   {
      if (x % i==0 && y % i == 0)
         count++;
      if (count == k)
         return i;
   }
 
   // If we reached small
   return -1;
}
 
// Driver code
int main()
{
   int x = 4, y = 24, k = 3;
   cout << findKHCF(x, y, k);
   return 0;
}

Java




// Java program to find kth
// common factor of two numbers
import java.lang.*;
 
class GFG {
     
// Returns k'th common factor of x and y.
static int findKHCF(int x, int y, int k) {
     
    // Find smaller of two numbers
    int small = Math.min(x, y);
 
    // Count common factors until we either
    // reach small or count becomes k.
    int count = 1;
    for (int i = 2; i <= small; i++) {
    if (x % i == 0 && y % i == 0)
        count++;
    if (count == k)
        return i;
    }
 
    // If we reached small
    return -1;
}
 
// Driver code
public static void main(String[] args) {
     
    int x = 4, y = 24, k = 3;
    System.out.print(findKHCF(x, y, k));
}
}
 
// This code is contributed by Anant Agarwal.

Python3




# Python program to find
# kth common factor
# of two numbers
 
# Returns k'th common
# factor of x and y.
def findKHCF(x,y,k):
 
    # Find smaller of two numbers
    small = min(x, y)
  
    # Count common factors
    # until we either
    # reach small or count
    # becomes k.
    count = 1
    for i in range(2,small+1):
    
        if (x % i==0 and y % i == 0):
            count=count + 1
        if (count == k):
            return i
    
  
    # If we reached small
    return -1
 
# Driver code
 
x = 4
y = 24
k = 3
print(findKHCF(x, y, k))
 
# This code is contributed
# by Anant Agarwal.

C#




// C# program to find kth
// common factor of two numbers
using System;
 
class GFG {
     
// Returns k'th common factor of x and y.
static int findKHCF(int x, int y, int k)
{
     
    // Find smaller of two numbers
    int small = Math.Min(x, y);
 
    // Count common factors until we either
    // reach small or count becomes k.
    int count = 1;
    for (int i = 2; i <= small; i++)
    {
        if (x % i == 0 && y % i == 0)
            count++;
        if (count == k)
            return i;
    }
 
    // If we reached small
    return -1;
}
 
// Driver code
public static void Main()
{
    int x = 4, y = 24, k = 3;
    Console.Write(findKHCF(x, y, k));
}
}
 
// This code is contributed by Nitin Mittal.

PHP




<?php
// PHP program to find kth
// common factor of two numbers
 
// Returns k'th common
// factor of x and y.
function findKCF($x, $y, $k)
{
// Find smaller of two numbers
$small = min($x, $y);
 
// Count common factors until we either
// reach small or count becomes k.
$count = 1;
for ($i = 2; $i <= $small; $i++)
{
    if ($x % $i == 0 && $y % $i == 0)
        $count++;
    if ($count == $k)
        return $i;
}
 
// If we reached small
return -1;
}
 
// Driver code
$x = 4; $y = 24; $k = 3;
echo findKCF($x, $y, $k);
 
// This code is contributed by nitin mittal.
?>

Javascript




<script>
 
// Javascript program to find kth
// common factor of two numbers
 
// Returns k'th common factor of x and y.
function findKHCF(x, y, k) {
       
    // Find smaller of two numbers
    let small = Math.min(x, y);
   
    // Count common factors until we either
    // reach small or count becomes k.
    let count = 1;
    for (let i = 2; i <= small; i++) {
    if (x % i == 0 && y % i == 0)
        count++;
    if (count == k)
        return i;
    }
   
    // If we reached small
    return -1;
}
      
// Driver code   
 
    let x = 4, y = 24, k = 3;
    document.write(findKHCF(x, y, k));
           
</script>

Output : 

4

Time complexity: O(n) where n is smallest among (x,y)

Auxiliary space: O(1)

This article is contributed by Afzal Ansari. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 


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