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; ` `} ` |

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## 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. ` |

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## 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. ` |

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## 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. ` |

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## 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. ` `?> ` |

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**Output :**

4

This article is contributed by **Afzal Ansari**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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