# Group all co-prime numbers from 1 to N

• Difficulty Level : Expert
• Last Updated : 08 Nov, 2021

Given an integer N, the task is to group numbers such that each group is mutually co-prime together with the total grouping is minimum.

Examples:

Input: N = 8
Output:
1 2 3
4 5
6 7
8

Input: N = 5
Output:
1 2 3
4 5

Approach: The key observation in this problem is two consecutive numbers are always co-prime. That is GCD(a, a+1) = 1. Another important observation is even numbers can’t be listed in one group. Because they will lead to the greatest common divisor of 2. Therefore, every consecutive even and odd numbers can be grouped into one group and 1 can be in any group because the greatest common divisor of numbers with 1 is always 1.

Below is the implementation of the above approach :

## C++

 `// C++ implementation to group``// mutually coprime numbers into``// one group with minimum group possible``#include``using` `namespace` `std;` `// Function to group the mutually``// co-prime numbers into one group``void` `mutually_coprime(``int` `n)``{``    ``if` `(n <= 3)``    ``{``        ` `        ``// Loop for the numbers less``        ``// than the 4``        ``for``(``int` `j = 1; j <= n; j++)``        ``{``            ``cout << j << ``" "``;``        ``}``        ``cout << ``"\n"``;``    ``}``    ``else``    ``{``        ` `        ``// Integers 1, 2 and 3 can be``        ``// grouped into one group``        ``cout << ``"1 2 3\n"``;``        ` `        ``for``(``int` `j = 4; j < n; j += 2)``        ``{``            ` `            ``// Consecutive even and``            ``// odd numbers``            ``cout << j << ``" "` `<< j + 1 << ``"\n"``;``        ``}``        ``if``(n % 2 == 0)``            ``cout << n << ``"\n"``;``    ``}``}` `// Driver Code        ``int` `main()``{``    ``int` `n = 9;``    ` `    ``// Function call``    ``mutually_coprime(n);``}` `// This code is contributed by yatinagg`

## Java

 `// Java implementation to group``// mutually coprime numbers into``// one group with minimum group possible``class` `GFG{``    ` `// Function to group the mutually``// co-prime numbers into one group``static` `void` `mutually_coprime(``int` `n)``{``    ``if` `(n <= ``3``)``    ``{``        ` `        ``// Loop for the numbers less``        ``// than the 4``        ``for``(``int` `j = ``1``; j < n + ``1``; j++)``           ``System.out.print(j + ``" "``);``        ``System.out.println();``    ``}``    ``else``    ``{``        ` `        ``// Integers 1, 2 and 3 can be``        ``// grouped into one group``        ``System.out.println(``"1 2 3"``);``        ``for``(``int` `j = ``4``; j < n; j += ``2``)``        ``{` `           ``// Consecutive even and``           ``// odd numbers``           ``System.out.println(j + ``" "` `+ (j + ``1``));``           ``if` `(n % ``2` `== ``0``)``           ``System.out.println(n);``        ``}``    ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``9``;` `    ``// Function Call``    ``mutually_coprime(n);``}``}` `// This code is contributed by sapnasingh4991`

## Python3

 `# Python3 implementation to group``# mutually coprime numbers into``# one group with minimum group possible` `# Function to group the mutually``# co-prime numbers into one group``def` `mutually_coprime (n):   ``    ``if` `( n <``=` `3``):``        ``# Loop for the numbers less``        ``# than the 4``        ``for` `j ``in` `range` `(``1``, n ``+` `1``):``            ``print` `(j, end ``=``" "``)``        ``print` `()``    ``else``:``        ``# Integers 1, 2 and 3 can be``        ``# grouped into one group``        ``print` `(``1``, ``2``, ``3``)``        ``for` `j ``in` `range` `( ``4``, n, ``2` `):``            ` `            ``# Consecutive even and``            ``# odd numbers``            ``print` `(j, ( j ``+` `1` `))``        ``if``(n ``%` `2` `=``=` `0``):        ``            ``print` `(n)` `# Driver Code           ``if` `__name__ ``=``=` `"__main__"``:``    ``n ``=` `9``    ` `    ``# Function Call``    ``mutually_coprime (n)`

## C#

 `// C# implementation to group``// mutually coprime numbers into``// one group with minimum group possible``using` `System;` `class` `GFG{``    ` `// Function to group the mutually``// co-prime numbers into one group``static` `void` `mutually_coprime(``int` `n)``{``    ``if` `(n <= 3)``    ``{``        ` `        ``// Loop for the numbers less``        ``// than the 4``        ``for``(``int` `j = 1; j < n + 1; j++)``           ``Console.Write(j + ``" "``);``           ` `        ``Console.WriteLine();``    ``}``    ``else``    ``{``        ` `        ``// ints 1, 2 and 3 can be``        ``// grouped into one group``        ``Console.WriteLine(``"1 2 3"``);``        ``for``(``int` `j = 4; j < n; j += 2)``        ``{``           ``// Consecutive even and``           ``// odd numbers``           ``Console.WriteLine(j + ``" "` `+ (j + 1));``            ` `           ``if` `(n % 2 == 0)``               ``Console.WriteLine(n);``        ``}``    ``}``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `n = 9;` `    ``// Function Call``    ``mutually_coprime(n);``}``}``// This code is contributed by sapnasingh4991`

## Javascript

 ``

Output:

```1 2 3
4 5
6 7
8 9         ```

Time Complexity: O(n)

Auxiliary Space: O(1)

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