# Generate K co-prime pairs of factors of a given number

Given two integers N and K, the task is to find K pair of factors of the number N such that the GCD of each pair of factors is 1.
Note: K co-prime factors always exist for the given number
Examples:

Input: N = 6, K = 1
Output: 2 3
Explanation:
Since 2 and 3 are both factors of 6 and gcd(2, 3) = 1.
Input: N = 120, K = 4
Output:
2 3
3 4
3 5
4 5

Naive Approach:
The simplest approach would be to check all the numbers upto N and check if the GCD of the pair is 1.
Time Complexity: O(N2
Space Complexity: O(1)
Linear Approach:
Find all possible divisors of N and store in another array. Traverse through the array to search for all possible coprime pairs from the array and print them.
Time Complexity: O(N)
Space Complexity: O(N)
Efficient Approach:
Follow the steps below to solve the problem:

• It can be observed that if GCD of any number, say x, with 1 is always 1, i.e. GCD(1, x) = 1.
• Since 1 will always be a factor of N, simply print any K factors of N with 1 as the coprime pairs.

Below is the implementation of the above approach.

## C++

 `// C++ implementation of ` `// the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function prints the ` `// required pairs ` `void` `FindPairs(``int` `n, ``int` `k) ` `{ ` `    ``// First co-prime pair ` `    ``cout << 1 << ``" "` `<< n << endl; ` ` `  `    ``// As a pair (1 n) has ` `    ``// already been Printed ` `    ``k--; ` ` `  `    ``for` `(``long` `long` `i = 2; ` `         ``i <= ``sqrt``(n); i++) { ` ` `  `        ``// If i is a factor of N ` `        ``if` `(n % i == 0) { ` ` `  `            ``cout << 1 << ``" "` `                 ``<< i << endl; ` `            ``k--; ` `            ``if` `(k == 0) ` `                ``break``; ` ` `  `            ``// Since (i, i) won't form ` `            ``// a coprime pair ` `            ``if` `(i != n / i) { ` `                ``cout << 1 << ``" "` `                     ``<< n / i << endl; ` `                ``k--; ` `            ``} ` `            ``if` `(k == 0) ` `                ``break``; ` `        ``} ` `    ``} ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` ` `  `    ``int` `N = 100; ` `    ``int` `K = 5; ` ` `  `    ``FindPairs(N, K); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of  ` `// the above approach  ` `import` `java.util.*; ` ` `  `class` `GFG{  ` ` `  `// Function prints the  ` `// required pairs  ` `static` `void` `FindPairs(``int` `n, ``int` `k)  ` `{  ` `     `  `    ``// First co-prime pair  ` `    ``System.out.print(``1` `+ ``" "` `+ n + ``"\n"``);  ` ` `  `    ``// As a pair (1 n) has  ` `    ``// already been Printed  ` `    ``k--;  ` ` `  `    ``for``(``long` `i = ``2``; i <= Math.sqrt(n); i++) ` `    ``{  ` `         `  `        ``// If i is a factor of N  ` `        ``if` `(n % i == ``0``) ` `        ``{  ` `            ``System.out.print(``1` `+ ``" "` `+ i + ``"\n"``);  ` `            ``k--;  ` `            ``if` `(k == ``0``)  ` `                ``break``;  ` ` `  `            ``// Since (i, i) won't form  ` `            ``// a coprime pair  ` `            ``if` `(i != n / i) ` `            ``{  ` `                ``System.out.print(``1` `+ ``" "` `+  ` `                             ``n / i + ``"\n"``);  ` `                ``k--;  ` `            ``}  ` `            ``if` `(k == ``0``)  ` `                ``break``;  ` `        ``}  ` `    ``}  ` `}  ` ` `  `// Driver Code  ` `public` `static` `void` `main(String[] args)  ` `{  ` `    ``int` `N = ``100``;  ` `    ``int` `K = ``5``;  ` ` `  `    ``FindPairs(N, K);  ` `} ` `}  ` ` `  `// This code is contributed by princiraj1992 `

## Python3

 `# Python3 implementation of ` `# the above approach ` `from` `math ``import` `sqrt ` ` `  `# Function prints the ` `# required pairs ` `def` `FindPairs(n, k): ` ` `  `    ``# First co-prime pair ` `    ``print``(``1``, n) ` ` `  `    ``# As a pair (1 n) has ` `    ``# already been Printed ` `    ``k ``-``=` `1` ` `  `    ``for` `i ``in` `range``(``2``, ``int``(sqrt(n)) ``+` `1``): ` ` `  `        ``# If i is a factor of N ` `        ``if``(n ``%` `i ``=``=` `0``): ` `            ``print``(``1``, i) ` ` `  `            ``k ``-``=` `1` `            ``if``(k ``=``=` `0``): ` `                ``break` ` `  `            ``# Since (i, i) won't form ` `            ``# a coprime pair ` `            ``if``(i !``=` `n ``/``/` `i): ` `                ``print``(``1``, n ``/``/` `i) ` `                ``k ``-``=` `1` ` `  `            ``if``(k ``=``=` `0``): ` `                ``break` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` ` `  `    ``N ``=` `100` `    ``K ``=` `5` ` `  `    ``FindPairs(N, K) ` ` `  `# This code is contributed by Shivam Singh `

## C#

 `// C# implementation of  ` `// the above approach  ` `using` `System; ` ` `  `class` `GFG{  ` ` `  `// Function prints the  ` `// required pairs  ` `static` `void` `FindPairs(``int` `n, ``int` `k)  ` `{  ` `     `  `    ``// First co-prime pair  ` `    ``Console.Write(1 + ``" "` `+ n + ``"\n"``);  ` ` `  `    ``// As a pair (1 n) has  ` `    ``// already been Printed  ` `    ``k--;  ` ` `  `    ``for``(``long` `i = 2; i <= Math.Sqrt(n); i++) ` `    ``{  ` `         `  `        ``// If i is a factor of N  ` `        ``if` `(n % i == 0) ` `        ``{  ` `            ``Console.Write(1 + ``" "` `+ i + ``"\n"``);  ` `            ``k--;  ` `            ``if` `(k == 0)  ` `                ``break``;  ` ` `  `            ``// Since (i, i) won't form  ` `            ``// a coprime pair  ` `            ``if` `(i != n / i) ` `            ``{  ` `                ``Console.Write(1 + ``" "` `+  ` `                          ``n / i + ``"\n"``);  ` `                ``k--;  ` `            ``}  ` `            ``if` `(k == 0)  ` `                ``break``;  ` `        ``}  ` `    ``}  ` `}  ` ` `  `// Driver Code  ` `public` `static` `void` `Main(String[] args)  ` `{  ` `    ``int` `N = 100;  ` `    ``int` `K = 5;  ` ` `  `    ``FindPairs(N, K);  ` `} ` `}  ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```1 100
1 2
1 50
1 4
1 25
```

Time Complexity: O(sqrt(N))
Auxilairy Space: O(1)

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Improved By : princiraj1992, Rajput-Ji