Given a number N, find the number of ways to represent this number as a sum of 2 or more consecutive natural numbers.

**Examples:**

Input :15 Output :3 15 can be represented as: 1+2+3+4+5 4+5+6 7+8 Input :10 Output :1 10 can only be represented as: 1+2+3+4

The idea is to represent N as a sequence of length L+1 as:

N = a + (a+1) + (a+2) + .. + (a+L)

=> N = (L+1)*a + (L*(L+1))/2

=> a = (N- L*(L+1)/2)/(L+1)

We substitute the values of L starting from 1 till L*(L+1)/2 < N

If we get 'a' as a natural number then the solution should be counted.

## C/C++

`// C++ program to count number of ways to express ` `// N as sum of consecutive numbers. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `long` `int` `countConsecutive(` `long` `int` `N) ` `{ ` ` ` `// constraint on values of L gives us the ` ` ` `// time Complexity as O(N^0.5) ` ` ` `long` `int` `count = 0; ` ` ` `for` `(` `long` `int` `L = 1; L * (L + 1) < 2 * N; L++) ` ` ` `{ ` ` ` `float` `a = (1.0 * N-(L * (L + 1)) / 2) / (L + 1); ` ` ` `if` `(a-(` `int` `)a == 0.0) ` ` ` `count++; ` ` ` `} ` ` ` `return` `count; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `long` `int` `N = 15; ` ` ` `cout << countConsecutive(N) << endl; ` ` ` `N = 10; ` ` ` `cout << countConsecutive(N) << endl; ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// A Java program to count number of ways ` `// to express N as sum of consecutive numbers. ` `public` `class` `SumConsecutiveNumber ` `{ ` ` ` `// Utility method to compute number of ways ` ` ` `// in which N can be represented as sum of ` ` ` `// consecutive number ` ` ` `static` `int` `countConsecutive(` `int` `N) ` ` ` `{ ` ` ` `// constraint on values of L gives us the ` ` ` `// time Complexity as O(N^0.5) ` ` ` `int` `count = ` `0` `; ` ` ` `for` `(` `int` `L = ` `1` `; L * (L + ` `1` `) < ` `2` `* N; L++) ` ` ` `{ ` ` ` `float` `a = (` `float` `) ((` `1.0` `* N-(L * (L + ` `1` `)) / ` `2` `) / (L + ` `1` `)); ` ` ` `if` `(a-(` `int` `)a == ` `0.0` `) ` ` ` `count++; ` ` ` `} ` ` ` `return` `count; ` ` ` `} ` ` ` ` ` `// Driver code to test above function ` ` ` `public` `static` `void` `main(String[] args) { ` ` ` `int` `N = ` `15` `; ` ` ` `System.out.println(countConsecutive(N)); ` ` ` `N = ` `10` `; ` ` ` `System.out.println(countConsecutive(N)); ` ` ` `} ` `} ` `// This code is contributed by Sumit Ghosh ` |

*chevron_right*

*filter_none*

## Python

`# Python program to count number of ways to ` `# express N as sum of consecutive numbers. ` ` ` `def` `countConsecutive(N): ` ` ` ` ` `# constraint on values of L gives us the ` ` ` `# time Complexity as O(N^0.5) ` ` ` `count ` `=` `0` ` ` `L ` `=` `1` ` ` `while` `( L ` `*` `(L ` `+` `1` `) < ` `2` `*` `N): ` ` ` `a ` `=` `(` `1.0` `*` `N ` `-` `(L ` `*` `(L ` `+` `1` `) ) ` `/` `2` `) ` `/` `(L ` `+` `1` `) ` ` ` `if` `(a ` `-` `int` `(a) ` `=` `=` `0.0` `): ` ` ` `count ` `+` `=` `1` ` ` `L ` `+` `=` `1` ` ` `return` `count ` ` ` `# Driver code ` ` ` `N ` `=` `15` `print` `countConsecutive(N) ` `N ` `=` `10` `print` `countConsecutive(N) ` ` ` `# This code is contributed by Sachin Bisht ` |

*chevron_right*

*filter_none*

## C#

`// A C# program to count number of ` `// ways to express N as sum of ` `// consecutive numbers. ` `using` `System; ` ` ` `public` `class` `GFG { ` ` ` ` ` `// Utility method to compute ` ` ` `// number of ways in which N ` ` ` `// can be represented as sum ` ` ` `// of consecutive number ` ` ` `static` `int` `countConsecutive(` `int` `N) ` ` ` `{ ` ` ` ` ` `// constraint on values of L ` ` ` `// gives us the time ` ` ` `// Complexity as O(N^0.5) ` ` ` `int` `count = 0; ` ` ` `for` `(` `int` `L = 1; L * (L + 1) ` ` ` `< 2 * N; L++) ` ` ` `{ ` ` ` `float` `a = (` `float` `) ((1.0 ` ` ` `* N-(L * (L + 1)) ` ` ` `/ 2) / (L + 1)); ` ` ` ` ` `if` `(a - (` `int` `)a == 0.0) ` ` ` `count++; ` ` ` `} ` ` ` ` ` `return` `count; ` ` ` `} ` ` ` ` ` `// Driver code to test above ` ` ` `// function ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `N = 15; ` ` ` `Console.WriteLine( ` ` ` `countConsecutive(N)); ` ` ` ` ` `N = 10; ` ` ` `Console.Write( ` ` ` `countConsecutive(N)); ` ` ` `} ` `} ` ` ` `// This code is contributed by ` `// nitin mittal. ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP program to count number ` `// of ways to express N as sum ` `// of consecutive numbers. ` ` ` `function` `countConsecutive(` `$N` `) ` `{ ` ` ` `// constraint on values ` ` ` `// of L gives us the ` ` ` `// time Complexity as O(N^0.5) ` ` ` `$count` `= 0; ` ` ` `for` `(` `$L` `= 1; ` ` ` `$L` `* (` `$L` `+ 1) < 2 * ` `$N` `; ` `$L` `++) ` ` ` `{ ` ` ` `$a` `= (int)(1.0 * ` `$N` `- (` `$L` `* ` ` ` `(int)(` `$L` `+ 1)) / 2) / (` `$L` `+ 1); ` ` ` `if` `(` `$a` `- (int)` `$a` `== 0.0) ` ` ` `$count` `++; ` ` ` `} ` ` ` `return` `$count` `; ` `} ` ` ` `// Driver Code ` `$N` `= 15; ` `echo` `countConsecutive(` `$N` `), ` `"\n"` `; ` `$N` `= 10; ` `echo` `countConsecutive(` `$N` `), ` `"\n"` `; ` ` ` `// This code is contributed by ajit ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

3 1

The Time complexity for this program is O(N^0.5), because of the condition in the for loop.

This article is contributed by **Pranav Marathe**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.

## Recommended Posts:

- Count ways to reach the n'th stair
- Longest Consecutive Subsequence
- Find subarray with given sum | Set 1 (Nonnegative Numbers)
- Calculate sum of all numbers present in a string
- Count the number of possible triangles
- Segregate Even and Odd numbers
- Count all possible paths from top left to bottom right of a mXn matrix
- Count Possible Decodings of a given Digit Sequence
- Count of distinct substrings of a string using Suffix Array
- Largest Sum Contiguous Subarray
- Find a pair with given sum in a Balanced BST
- Find the Missing Number
- Find the number of islands | Set 1 (Using DFS)
- VISA Interview Experience (On-Campus)