Find the count of natural Hexadecimal numbers of size N

Given an integer N, the task is to find the count of natural Hexadecimal numbers with N digits.

Examples:

Input: N = 1
Output: 15



Input: N = 2
Output: 240

Approach: It can be observed that for the values of N = 1, 2, 3, …, a series will be formed as 15, 240, 3840, 61440, 983040, 15728640, … which is a GP series whose common ratio is 16 and a = 15.

Hence the nth term will be 15 * pow(16, n – 1).

So, the count of n-digit natural hexadecimal numbers will be 15 * pow(16, n – 1).

Below is the implementation of the above approach:

C++

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// C++ implementation of the above approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the count of n-digit 
// natural hexadecimal numbers
int count(int n)
{
    return 15 * pow(16, n - 1);
}
  
// Driver code
int main()
{
    int n = 2;
    cout << count(n);
    return 0;
}

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Java

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// Java implementation of the approach
class GFG 
{
  
// Function to return the count of n-digit 
// natural hexadecimal numbers
static int count(int n)
{
    return (int) (15 * Math.pow(16, n - 1));
}
  
// Driver code
public static void main(String args[]) 
{
    int n = 2;
    System.out.println(count(n));
}
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 implementation of the above approach 
  
# Function to return the count of n-digit 
# natural hexadecimal numbers 
def count(n) : 
  
    return 15 * pow(16, n - 1); 
  
# Driver code 
if __name__ == "__main__"
  
    n = 2
    print(count(n));
      
# This code is contributed by AnkitRai01

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C#

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// C# implementation of the approach
using System;
      
class GFG 
{
  
    // Function to return the count of n-digit 
    // natural hexadecimal numbers
    static int count(int n)
    {
        return (int) (15 * Math.Pow(16, n - 1));
    }
      
    // Driver code
    public static void Main(String []args) 
    {
        int n = 2;
        Console.WriteLine(count(n));
    }
}
  
// This code is contributed by 29AjayKumar

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Output:

240

Time Complexity: O(1)



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Improved By : AnkitRai01, 29AjayKumar