# Count of matrices (of different orders) with given number of elements

Given a number N denotes the total number of elements in a matrix, the task is to print all possible order of matrix. An order is a pair (m, n) of integers where m is number of rows and n is number of columns. For example, if the number of elements is 8 then all possible orders are:
(1, 8), (2, 4), (4, 2), (8, 1).
Examples:

Input: N = 8
Output: (1, 2) (2, 4) (4, 2) (8, 1)
Input: N = 100
Output:
(1, 100) (2, 50) (4, 25) (5, 20) (10, 10) (20, 5) (25, 4) (50, 2) (100, 1)

Approach:
A matrix is said to be of order m x n if it has m rows and n columns. The total number of elements in a matrix is equal to (m*n). So we start from 1 and check one by one if it divides N(the total number of elements). If it divides, it will be one possible order.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach` `#include ` `using` `namespace` `std;`   `// Function to print all possible order` `void` `printAllOrder(``int` `n)` `{` `    ``// total number of elements in a matrix ` `    ``// of order m * n is equal (m*n)` `    ``// where m is number of rows and n is ` `    ``// number of columns` `    ``for` `(``int` `i = 1; i <= n; i++) {`   `        ``// if n is divisible by i then i` `        ``// and n/i will be the one` `        ``// possible order of the matrix` `        ``if` `(n % i == 0) {`   `            ``// print the given format` `            ``cout << i << ``" "` `<< n / i << endl;` `        ``}` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 10;` `    ``printAllOrder(n);` `    ``return` `0;` `}`

## Java

 `// Java implementation of the above approach`     `class` `GFG` `    ``{` `    ``// Function to print all possible order` `    ``static` `void` `printAllOrder(``int` `n)` `    ``{` `        ``// total number of elements in a matrix ` `        ``// of order m * n is equal (m*n)` `        ``// where m is number of rows and n is ` `        ``// number of columns` `        ``for` `(``int` `i = ``1``; i <= n; i++) {` `    `  `            ``// if n is divisible by i then i` `            ``// and n/i will be the one` `            ``// possible order of the matrix` `            ``if` `(n % i == ``0``) {` `    `  `                ``// print the given format` `                ``System.out.println( i + ``" "` `+ n / i );` `            ``}` `        ``}` `    ``}` `    `  `    ``// Driver code` `    ``public` `static` `void` `main(String []args)` `    ``{` `        ``int` `n = ``10``;` `        ``printAllOrder(n);` `        `  `    ``}`   `}`     `// This code is contributed by ihritik`

## Python

 `# Python implementation of the above approach`   `# Function to print all possible order` `def` `printAllOrder(n):`   `    ``# total number of elements in a matrix ` `    ``# of order m * n is equal (m*n)` `    ``# where m is number of rows and n is ` `    ``# number of columns` `    ``for` `i ``in` `range``(``1``,n``+``1``):`   `        ``# if n is divisible by i then i` `        ``# and n/i will be the one` `        ``# possible order of the matrix` `        ``if` `(n ``%` `i ``=``=` `0``) :`   `            ``# print the given format` `            ``print``( i ,n ``/``/` `i )` `        `  `    `      `# Driver code` `n ``=` `10` `printAllOrder(n)`     `# This code is contributed by ihritik`

## C#

 `// C# implementation of the above approach`   `using` `System;` `class` `GFG` `    ``{` `    ``// Function to print all possible order` `    ``static` `void` `printAllOrder(``int` `n)` `    ``{` `        ``// total number of elements in a matrix ` `        ``// of order m * n is equal (m*n)` `        ``// where m is number of rows and n is ` `        ``// number of columns` `        ``for` `(``int` `i = 1; i <= n; i++) {` `    `  `            ``// if n is divisible by i then i` `            ``// and n/i will be the one` `            ``// possible order of the matrix` `            ``if` `(n % i == 0) {` `    `  `                ``// print the given format` `                ``Console.WriteLine( i + ``" "` `+ n / i );` `            ``}` `        ``}` `    ``}` `    `  `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `n = 10;` `        ``printAllOrder(n);` `        `  `    ``}`   `}`   `// This code is contributed by ihritik`

## PHP

 ``

## Javascript

 ``

Output:

```1 10
2 5
5 2
10 1```

Time Complexity: O(n)

Auxiliary Space: O(1)

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