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Count of matrices (of different orders) with given number of elements
  • Last Updated : 13 May, 2021

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 <iostream>
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




<?php
// PHP implementation of the above approach
 
// Function to print all possible order
function 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 = 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
            echo $i, " ", ($n / $i), "\n";
        }
    }
}
 
// Driver code
$n = 10;
printAllOrder($n);
 
// This code is contributed by Ryuga
?>

Javascript




<script>
// Java Script implementation of the above approach
 
 
    // Function to print all possible order
    function 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 (let 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
                document.write( i + " " + n / i+"<br>" );
            }
        }
    }
     
    // Driver code
     
        let n = 10;
        printAllOrder(n);
         
     
// This code is contributed by sravan
</script>
Output: 
1 10
2 5
5 2
10 1

 

Time Complexity: O(n)

Auxiliary Space: O(1)

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