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Rectangular (or Pronic) Numbers

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The numbers that can be arranged to form a rectangle are called Rectangular Numbers (also known as Pronic numbers). The first few rectangular numbers are: 
0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462 . . . . . . 
Given a number n, find n-th rectangular number.
Examples: 
 

Input : 1
Output : 2

Input : 4
Output : 20

Input : 5
Output : 30


 


The number 2 is a rectangular number because it is 1 row by 2 columns. The number 6 is a rectangular number because it is 2 rows by 3 columns, and the number 12 is a rectangular number because it is 3 rows by 4 columns. 
If we observe these numbers carefully, we can notice that n-th rectangular number is n(n+1).
 


 

C++

// CPP Program to find n-th rectangular number
#include <bits/stdc++.h>
using namespace std;
  
// Returns n-th rectangular number
int findRectNum(int n)
{
    return n * (n + 1);
}
  
// Driver code
int main()
{
    int n = 6;
    cout << findRectNum(n);
    return 0;
}

                    

Java

// Java Program to find n-th rectangular number
import java.io.*;
  
class GFG {
  
    // Returns n-th rectangular number
    static int findRectNum(int n)
    {
        return n * (n + 1);
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int n = 6;
        System.out.println(findRectNum(n));
    }
}
  
// This code is contributed by vt_m.

                    

C#

// C# Program to find n-th rectangular number
  
using System;
  
class GFG {
  
    // Returns n-th rectangular number
    static int findRectNum(int n)
    {
        return n * (n + 1);
    }
  
    // Driver code
    public static void Main()
    {
        int n = 6;
        Console.Write(findRectNum(n));
    }
}
  
// This code is contributed by vt_m.

                    

Python

# Python3 Program to find n-th rectangular number
  
# Returns n-th rectangular number
def findRectNum(n):
    return n*(n + 1)
  
# Driver code 
n = 6
print (findRectNum(n))
  
# This code is contributed by Shreyanshi Arun.

                    

PHP

<?php
// PHP Program to find n-th
// rectangular number
  
// Returns n-th rectangular
// number
function findRectNum($n)
{
    return $n * ($n + 1);
}
  
    // Driver Code
    $n = 6;
    echo findRectNum($n);
      
// This code is contributed by ajit
?>

                    

Javascript

<script>
  
// Javascript Program to find n-th rectangular number 
  
// Returns n-th rectangular number 
function findRectNum(n) 
    return n * (n + 1); 
  
// Driver code 
var n = 6; 
document.write(findRectNum(n));
  
// This code is contributed by noob2000.
</script>

                    

Output: 
 

42

Time complexity: O(1) since performing constant operations

Space complexity: O(1) since using constant space for variables


Check if a given number is Pronic | Efficient Approach


 



Last Updated : 15 Sep, 2023
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