# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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

 ` `

Output :

```4
```

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Improved By : nitin mittal

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