# Find two proper factors of N such that their sum is coprime with N

Given an integer **N**, you have to find two proper factors of **N** such that their sum is coprime with the given integer **N**. If no such factors exist, print -1.

**Examples:**

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Input:N = 15Output:3, 5Explanation:3 and 5 are the proper factors of 15 and 3+5 -> 8 is coprime with 15.

Input:N = 4Output:-1Explanation:there are no proper factors that satisfy the required conditions

**Naive Approach:** Generate a list of all the proper factors of N and for each possible pair, check if their sum is coprime with N i.e. GCD(sum of pair of integers, N) = 1. Here GCD means Greatest Common Divisor.

**Efficient Approach:** If two numbers **A** and **B** are coprime then their sum is coprime with their product. Keeping that in mind, find all the factors of N and for each factor **d1**, calculate the largest factor of N, **d2** that is coprime with **d1**. To calculate d2, simply divide **N **with** d1** until **N%d1 **!= **0**. Finally, check if **d1 **and** d2** are proper factors of **N** or not (i.e., d1>1 and d2>1).

Below is the implementation of the above approach:

## C++

`// C++ Program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find two proper` `// factors of N such that their` `// sum is coprime with N` `void` `printFactors(` `int` `n)` `{` ` ` `// Find factors in sorted order` ` ` `for` `(` `int` `i = 2; i <= ` `sqrt` `(n); i++) {` ` ` `if` `(n % i == 0) {` ` ` `int` `d1 = i, d2 = n;` ` ` `// Find largest value of d2 such` ` ` `// that d1 and d2 are co-prime` ` ` `while` `(d2 % d1 == 0) {` ` ` `d2 = d2 / d1;` ` ` `}` ` ` `// Check if d1 and d2 are proper` ` ` `// factors of N` ` ` `if` `(d1 > 1 && d2 > 1) {` ` ` `// Print answer` ` ` `cout << d1 << ` `", "` `<< d2;` ` ` `return` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `// No such factors exist` ` ` `cout << -1;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `N = 10;` ` ` `// Function Call` ` ` `printFactors(N);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `class` `GFG{` `// Function to find two proper` `// factors of N such that their` `// sum is coprime with N ` `static` `void` `printFactors(` `int` `n)` `{` ` ` ` ` `// Find factors in sorted order` ` ` `for` `(` `int` `i = ` `2` `; i <= (` `int` `)Math.sqrt(n); i++)` ` ` `{` ` ` `if` `(n % i == ` `0` `)` ` ` `{` ` ` `int` `d1 = i, d2 = n;` ` ` `// Find largest value of d2 such` ` ` `// that d1 and d2 are co-prime` ` ` `while` `(d2 % d1 == ` `0` `)` ` ` `{` ` ` `d2 = d2 / d1;` ` ` `}` ` ` `// Check if d1 and d2 are proper` ` ` `// factors of N` ` ` `if` `(d1 > ` `1` `&& d2 > ` `1` `)` ` ` `{` ` ` ` ` `// Print answer` ` ` `System.out.print(d1 + ` `", "` `+ d2);` ` ` `return` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `// No such factors exist` ` ` `System.out.print(-` `1` `);` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `10` `;` ` ` ` ` `// Function Call` ` ` `printFactors(N);` `}` `}` `// This code is contributed by Potta Lokesh` |

## Python3

`# Python Program for the above approach` `import` `math` `# Function to find two proper` `# factors of N such that their` `# sum is coprime with N` `def` `printFactors(n):` ` ` `# Find factors in sorted order` ` ` `for` `i ` `in` `range` `(` `2` `, ` `int` `(math.sqrt(n))` `+` `1` `):` ` ` `if` `(n ` `%` `i ` `=` `=` `0` `):` ` ` `d1 ` `=` `i` ` ` `d2 ` `=` `n` ` ` ` ` `# Find largest value of d2 such` ` ` `# that d1 and d2 are co-prime` ` ` `while` `(d2 ` `%` `d1 ` `=` `=` `0` `):` ` ` `d2 ` `=` `d2 ` `/` `/` `d1` ` ` ` ` `# Check if d1 and d2 are proper` ` ` `# factors of N` ` ` `if` `(d1 > ` `1` `and` `d2 > ` `1` `):` ` ` ` ` `# Print answer` ` ` `print` `(d1, d2, sep` `=` `", "` `)` ` ` `return` ` ` `# No such factors exist` ` ` `print` `(` `-` `1` `)` `# Driver code` `N ` `=` `10` `# Function Call` `printFactors(N)` ` ` `# This code is contributed by Shivani` |

## C#

`// C# Program for the above approach` `using` `System;` `using` `System.Collections.Generic;` `class` `GFG{` `// Function to find two proper` `// factors of N such that their` `// sum is coprime with N` `static` `void` `printFactors(` `int` `n)` `{` ` ` `// Find factors in sorted order` ` ` `for` `(` `int` `i = 2; i <= (` `int` `)Math.Sqrt(n); i++) {` ` ` `if` `(n % i == 0) {` ` ` `int` `d1 = i, d2 = n;` ` ` `// Find largest value of d2 such` ` ` `// that d1 and d2 are co-prime` ` ` `while` `(d2 % d1 == 0) {` ` ` `d2 = d2 / d1;` ` ` `}` ` ` `// Check if d1 and d2 are proper` ` ` `// factors of N` ` ` `if` `(d1 > 1 && d2 > 1)` ` ` `{` ` ` ` ` `// Print answer` ` ` `Console.Write(d1 + ` `", "` `+d2);` ` ` `return` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `// No such factors exist` ` ` `Console.Write(-1);` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `int` `N = 10;` ` ` ` ` `// Function Call` ` ` `printFactors(N);` `}` `}` `// This code is contributed by ipg2016107.` |

## Javascript

`<script>` `// Javascript Program for the above approach` `// Function to find two proper` `// factors of N such that their` `// sum is coprime with N` `function` `printFactors(n) {` ` ` `// Find factors in sorted order` ` ` `for` `(let i = 2; i <= Math.sqrt(n); i++) {` ` ` `if` `(n % i == 0) {` ` ` `let d1 = i,` ` ` `d2 = n;` ` ` `// Find largest value of d2 such` ` ` `// that d1 and d2 are co-prime` ` ` `while` `(d2 % d1 == 0) {` ` ` `d2 = Math.floor(d2 / d1);` ` ` `}` ` ` `// Check if d1 and d2 are proper` ` ` `// factors of N` ` ` `if` `(d1 > 1 && d2 > 1) {` ` ` `// Print answer` ` ` `document.write(d1 + ` `", "` `+ d2);` ` ` `return` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `// No such factors exist` ` ` `document.write(-1);` `}` `// Driver code` `let N = 10;` `// Function Call` `printFactors(N);` `// This code is contributed by _saurabh_jaiswal.` `</script>` |

**Output:**

2, 5

**Time Complexity:** *O(√N)***Auxiliary Space:** *O(1)*