# Print the kth common factor of two numbers

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.

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