# Largest number that divides x and is co-prime with y

Given two positive numbers x and y. Find the maximum valued integer a such that:

1. a divides x i.e. x % a = 0
2. a and y are co-prime i.e. gcd(a, y) = 1

Examples :

```Input : x = 15
y = 3
Output : a = 5
Explanation: 5 is the max integer
which satisfies both the conditions.
15 % 5 =0
gcd(5, 3) = 1
Hence, output is 5.

Input : x = 14
y = 28
Output : a = 1
Explanation: 14 % 1 =0
gcd(1, 28) = 1
Hence, output is 1.
```

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

Approach: Here, first we will remove the common factors of x and y from x by finding the greatest common divisor (gcd) of x and y and dividing x with that gcd.
Mathematically:

` x = x / gcd(x, y) —— STEP1 `

Now, we repeat STEP1 till we get gcd(x, y) = 1.
At last, we return a = x

## C++

 `// CPP program to find the ` `// Largest Coprime Divisor ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Recursive function to return gcd ` `// of a and b ` `int` `gcd(``int` `a, ``int` `b) ` `{ ` `    ``// Everything divides 0 ` `    ``if` `(a == 0 || b == 0) ` `        ``return` `0; ` ` `  `    ``// base case ` `    ``if` `(a == b) ` `        ``return` `a; ` ` `  `    ``// a is greater ` `    ``if` `(a > b) ` `        ``return` `gcd(a - b, b); ` `    ``return` `gcd(a, b - a); ` `} ` ` `  `// function to find largest ` `// coprime divisor ` `int` `cpFact(``int` `x, ``int` `y) ` `{ ` `    ``while` `(gcd(x, y) != 1) { ` `        ``x = x / gcd(x, y); ` `    ``} ` `    ``return` `x; ` `} ` ` `  `// divisor code ` `int` `main() ` `{ ` `    ``int` `x = 15; ` `    ``int` `y = 3; ` `    ``cout << cpFact(x, y) << endl; ` `    ``x = 14; ` `    ``y = 28; ` `    ``cout << cpFact(x, y) << endl; ` `    ``x = 7; ` `    ``y = 3; ` `    ``cout << cpFact(x, y); ` `    ``return` `0; ` `} `

## Java

 `// java program to find the ` `// Largest Coprime Divisor ` `import` `java.io.*; ` ` `  `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``; ` ` `  `        ``// base case ` `        ``if` `(a == b) ` `            ``return` `a; ` ` `  `        ``// a is greater ` `        ``if` `(a > b) ` `            ``return` `gcd(a - b, b); ` `        ``return` `gcd(a, b - a); ` `    ``} ` ` `  `    ``// function to find largest ` `    ``// coprime divisor ` `    ``static` `int` `cpFact(``int` `x, ``int` `y) ` `    ``{ ` `        ``while` `(gcd(x, y) != ``1``) { ` `            ``x = x / gcd(x, y); ` `        ``} ` `        ``return` `x; ` `    ``} ` ` `  `    ``// divisor code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `x = ``15``; ` `        ``int` `y = ``3``; ` `        ``System.out.println(cpFact(x, y)); ` `        ``x = ``14``; ` `        ``y = ``28``; ` `        ``System.out.println(cpFact(x, y)); ` `        ``x = ``7``; ` `        ``y = ``3``; ` `        ``System.out.println(cpFact(x, y)); ` `    ``} ` `} ` ` `  `// This article is contributed by vt_m. `

## Python3

 `# Python3 code to find the ` `# Largest Coprime Divisor ` ` `  `# Recursive function to return ` `# gcd of a and b ` `def` `gcd (a, b): ` `     `  `    ``# Everything divides 0 ` `    ``if` `a ``=``=` `0` `or` `b ``=``=` `0``: ` `        ``return` `0` `     `  `    ``# base case ` `    ``if` `a ``=``=` `b: ` `        ``return` `a ` `         `  `    ``# a is greater ` `    ``if` `a > b: ` `        ``return` `gcd(a ``-` `b, b) ` `     `  `    ``return` `gcd(a, b ``-` `a) ` ` `  `# function to find largest ` `# coprime divisor ` `def` `cpFact(x, y): ` `    ``while` `gcd(x, y) !``=` `1``: ` `        ``x ``=` `x ``/` `gcd(x, y) ` `    ``return` `int``(x) ` `     `  `# divisor code ` `x ``=` `15` `y ``=` `3` `print``(cpFact(x, y)) ` `x ``=` `14` `y ``=` `28` `print``(cpFact(x, y)) ` `x ``=` `7` `y ``=` `3` `print``(cpFact(x, y)) ` ` `  `# This code is contributed by "Sharad_Bhardwaj". `

## C#

 `// C# program to find the ` `// Largest Coprime Divisor ` `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; ` ` `  `        ``// base case ` `        ``if` `(a == b) ` `            ``return` `a; ` ` `  `        ``// a is greater ` `        ``if` `(a > b) ` `            ``return` `gcd(a - b, b); ` ` `  `        ``return` `gcd(a, b - a); ` `    ``} ` ` `  `    ``// function to find largest ` `    ``// coprime divisor ` `    ``static` `int` `cpFact(``int` `x, ``int` `y) ` `    ``{ ` `        ``while` `(gcd(x, y) != 1) { ` `            ``x = x / gcd(x, y); ` `        ``} ` ` `  `        ``return` `x; ` `    ``} ` ` `  `    ``// divisor code ` `    ``public` `static` `void` `Main() ` `    ``{ ` ` `  `        ``int` `x = 15; ` `        ``int` `y = 3; ` `        ``Console.WriteLine(cpFact(x, y)); ` ` `  `        ``x = 14; ` `        ``y = 28; ` `        ``Console.WriteLine(cpFact(x, y)); ` ` `  `        ``x = 7; ` `        ``y = 3; ` `        ``Console.WriteLine(cpFact(x, y)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` ``\$b``) ` `        ``return` `gcd(``\$a` `- ``\$b``, ``\$b``); ` `    ``return` `gcd(``\$a``, ``\$b` `- ``\$a``); ` `} ` ` `  `// function to find largest ` `// coprime divisor ` `function` `cpFact( ``\$x``, ``\$y``) ` `{ ` `    ``while` `(gcd(``\$x``, ``\$y``) != 1)  ` `    ``{ ` `        ``\$x` `= ``\$x` `/ gcd(``\$x``, ``\$y``); ` `    ``} ` `    ``return` `\$x``; ` `} ` ` `  `// Driver Code ` `\$x` `= 15; ` `\$y` `= 3; ` `echo` `cpFact(``\$x``, ``\$y``), ``"\n"``; ` `\$x` `= 14; ` `\$y` `= 28; ` `echo` `cpFact(``\$x``, ``\$y``), ``"\n"``; ` `\$x` `= 7; ` `\$y` `= 3; ` `echo` `cpFact(``\$x``, ``\$y``); ` ` `  `// This code is contributed by aj_36 ` `?> `

Output :

```5
1
7
```

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