Natural Numbers

29 Jun, 2022
Counting numbers like 1, 2, 3, 4, 5, 6 ... Basically, all integers greater than 0 are natural numbers. 
Fact about Natural numbers 
They are whole numbers (called integers), and never less than zero (i.e. positive numbers)The next possible natural number can be found by adding 1 to the current natural numberThe natural numbers are the ordinary numbers, 1, 2, 3, etc., with which we count.The number zero is sometimes considered to be a natural number. Not always because no one counts starting with zero, 0, 1, 2, 3.GCD of all other natural numbers with a prime is always one.The natural numbers can be defined formally by relating them to sets. Then, zero is the number of elements in the empty set; 1 is the number of elements in the set containing one natural number; and so on.
They are whole numbers (called integers), and never less than zero (i.e. positive numbers)
The next possible natural number can be found by adding 1 to the current natural number
The natural numbers are the ordinary numbers, 1, 2, 3, etc., with which we count.
The number zero is sometimes considered to be a natural number. Not always because no one counts starting with zero, 0, 1, 2, 3.
GCD of all other natural numbers with a prime is always one.
The natural numbers can be defined formally by relating them to sets. Then, zero is the number of elements in the empty set; 1 is the number of elements in the set containing one natural number; and so on.
How to print sum of n natural Numbers?  
Using Recursion
Given a number n, find sum of first n natural numbers. To calculate the sum, we will use a recursive function recur_sum().
Examples :  
Input : 3
Output : 6
Explanation : 1 + 2 + 3 = 6

Input : 5
Output : 15
Explanation : 1 + 2 + 3 + 4 + 5 = 15
C++
Java
Python
C#
PHP
Javascript
// C++ program to find the// sum of natural numbers up// to n using recursion#include <iostream>using namespace std; // Returns sum of first// n natural numbersint recurSum(int n){    if (n <= 1)        return n;    return n + recurSum(n - 1);} // Driver codeint main(){    int n = 5;    cout << recurSum(n);    return 0;}
// Java program to find the// sum of natural numbers up// to n using recursionimport java.util.*;import java.lang.*; class GFG{     // Returns sum of first    // n natural numbers    public static int recurSum(int n)    {        if (n <= 1)            return n;        return n + recurSum(n - 1);    }         // Driver code    public static void main(String args[])    {        int n = 5;        System.out.println(recurSum(n));    }}
# Python code to find sum# of natural numbers upto# n using recursion # Returns sum of first# n natural numbersdef recurSum(n):    if n <= 1:        return n    return n + recurSum(n - 1) # Driver coden = 5print(recurSum(n))
// C# program to find the// sum of natural numbers// up to n using recursionusing System; class GFG{     // Returns sum of first    // n natural numbers    public static int recurSum(int n)    {        if (n <= 1)            return n;        return n + recurSum(n - 1);    }         // Driver code    public static void Main()    {        int n = 5;        Console.WriteLine(recurSum(n));    }}
<?php// PHP program to find the// sum of natural numbers// up to n using recursion // Returns sum of first// n natural numbersfunction recurSum($n){    if ($n <= 1)        return $n;    return $n + recurSum($n - 1);} // Driver code$n = 5;echo(recurSum($n)); ?>
<script> // JavaScript program to find the// sum of natural numbers// up to n using recursion // Returns sum of first// n natural numbersfunction recurSum(n){    if (n <= 1)        return n;    return n + recurSum(n - 1);} // Driver coden = 5;document.write(recurSum(n)); </script>
Output : 
15 
Time Complexity: O(n)
Auxiliary Space: O(n)
Using Loop
A simple solution is to do following. 
1) Initialize : sum = 0
2) Run a loop from x = 1 to n and 
   do following in loop.
     sum = sum + x  
C++
Java
Python
C#
PHP
Javascript
// CPP program to find sum of first// n natural numbers.#include<iostream>using namespace std; // Returns sum of first n natural// numbersint findSum(int n){   int sum = 0;   for (int x=1; x<=n; x++)     sum = sum + x;   return sum;} // Driver codeint main(){  int n = 5;  cout << findSum(n);  return 0;}
// JAVA program to find sum of first// n natural numbers.import java.io.*; class GFG{     // Returns sum of first n natural    // numbers    static int findSum(int n)    {        int sum = 0;        for (int x = 1; x <= n; x++)            sum = sum + x;        return sum;    }     // Driver code    public static void main(String args[])    {        int n = 5;        System.out.println(findSum(n));    }}
# PYTHON program to find sum of first# n natural numbers. # Returns sum of first n natural# numbersdef findSum(n) :    sum = 0    x = 1    while x <=n :        sum = sum + x        x = x + 1    return sum  # Driver code n = 5print findSum(n)
// C# program to find sum of first// n natural numbers.using System; class GFG{     // Returns sum of first n natural    // numbers    static int findSum(int n)    {        int sum = 0;        for (int x = 1; x <= n; x++)            sum = sum + x;        return sum;    }     // Driver code    public static void Main()    {        int n = 5;        Console.Write(findSum(n));    }}
<?php// PHP program to find sum of first// n natural numbers. // Returns sum of first n natural// numbersfunction findSum($n){$sum = 0;for ($x = 1; $x <= $n; $x++)    $sum = $sum + $x;return $sum;} // Driver code$n = 5;echo findSum($n);  ?>
<script>// JavaScript program to find the// sum of natural numbers// up to n using recursion // Returns sum of first// n natural numbersfunction findSum(n){let sum = 0;for (x = 1; x <= n; x++)    sum = sum + x;return sum;} // Driver coden = 5;document.write(findSum(n)); // This code is contributed by sravan kumar </script>
Output : 
15
Time Complexity: O(n)
Auxiliary Space: O(1)
Using Sum of n terms formula
Formula for finding sum of n natural numbers is given by n*(n+1)/2 which implies if the formula is used the program returns output faster than it would take iterating over loop or recursion. Time complexity is O(1). Referral Link Program to find sum of n natural numbers
More problems related to Natural Number:  
Count natural numbers whose all permutations are greater than that number
Sum of squares of first n natural numbers
Sum of cubes of even and odd natural numbers
LCM of First n Natural Numbers
Sum of squares of first n natural numbers
 
PranayRaju
sravankumar8128
singghakshay
rishav1329
number-theory
Numbers
Mathematical
number-theory
Mathematical
Numbers
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.