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Sum of numbers from 1 to N which are divisible by 3 or 4
• Last Updated : 26 Oct, 2018

Given a number N. The task is to find the sum of all those numbers from 1 to N that are divisible by 3 or by 4.

Examples:

```Input : N = 5
Output : 7
sum = 3 + 4

Input : N = 12
Output : 42
sum = 3 + 4 + 6 + 8 + 9 + 12
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: To solve the problem, follow the below steps:

1. Find the sum of numbers that are divisible by 3 upto N. Denote it by S1.
2. Find the sum of numbers that are divisible by 4 upto N. Denote it by S2.
3. Find the sum of numbers that are divisible by 12(3*4) upto N. Denote it by S3.
4. The final answer will be S1 + S2 – S3.

In order to find the sum, we can use the general formula of A.P. which is:

```Sn = (n/2) * {2*a + (n-1)*d}

Where,
n -> total number of terms
a -> first term
d -> common difference
```

For S1: The total numbers that will be divisible by 3 upto N will be N/3 and the series will be 3, 6, 9, 12, ….

```Hence,
S1 = ((N/3)/2) * (2 * 3 + (N/3 - 1) * 3)
```

For S2: The total numbers that will be divisible by 4 up to N will be N/4 and the series will be 4, 8, 12, 16, …...

```Hence,
S2 = ((N/4)/2) * (2 * 4 + (N/4 - 1) * 4)
```

For S3: The total numbers that will be divisible by 12 upto N will be N/12.

```Hence,
S3 = ((N/12)/2) * (2 * 12 + (N/12 - 1) * 12)
```

Therefore, the result will be:

```S = S1 + S2 - S3
```

Below is the implementation of the above approach:

## C++

 `// C++ program to find sum of numbers from 1 to N``// which are divisible by 3 or 4``#include ``using` `namespace` `std;`` ` `// Function to calculate the sum``// of numbers divisible by 3 or 4``int` `sum(``int` `N)``{``    ``int` `S1, S2, S3;`` ` `    ``S1 = ((N / 3)) * (2 * 3 + (N / 3 - 1) * 3) / 2;``    ``S2 = ((N / 4)) * (2 * 4 + (N / 4 - 1) * 4) / 2;``    ``S3 = ((N / 12)) * (2 * 12 + (N / 12 - 1) * 12) / 2;`` ` `    ``return` `S1 + S2 - S3;``}`` ` `// Driver code``int` `main()``{``    ``int` `N = 20;`` ` `    ``cout << sum(12);`` ` `    ``return` `0;``}`

## Java

 `// Java program to find sum of numbers from 1 to N ``// which are divisible by 3 or 4 ``class` `GFG{`` ` `// Function to calculate the sum ``// of numbers divisible by 3 or 4 ``static` `int` `sum(``int` `N) ``{ ``    ``int` `S1, S2, S3; `` ` `    ``S1 = ((N / ``3``)) * (``2` `* ``3` `+ (N / ``3` `- ``1``) * ``3``) / ``2``; ``    ``S2 = ((N / ``4``)) * (``2` `* ``4` `+ (N / ``4` `- ``1``) * ``4``) / ``2``; ``    ``S3 = ((N / ``12``)) * (``2` `* ``12` `+ (N / ``12` `- ``1``) * ``12``) / ``2``; `` ` `    ``return` `S1 + S2 - S3; ``} `` ` `// Driver code `` ``public` `static` `void` `main (String[] args) {``    ``int` `N = ``20``; `` ` `    ``System.out.print(sum(``12``)); ``}`` ` `} `

## Python3

 `# Python3 program to find sum of numbers ``# from 1 to N``# which are divisible by 3 or 4`` ` `# Function to calculate the sum ``# of numbers divisible by 3 or 4 ``def` `sum``(N):`` ` `    ``global` `S1,S2,S3`` ` `    ``S1 ``=` `(((N ``/``/` `3``)) ``*` `         ``(``2` `*` `3` `+` `(N ``/``/``3` `-` `1``) ``*` `3``) ``/``/``2``)``    ``S2 ``=` `(((N ``/``/` `4``)) ``*` `         ``(``2` `*` `4` `+` `(N ``/``/` `4` `-` `1``) ``*` `4``) ``/``/` `2``)``    ``S3 ``=` `(((N ``/``/` `12``)) ``*` `         ``(``2` `*` `12` `+` `(N ``/``/` `12` `-` `1``) ``*` `12``) ``/``/` `2``)`` ` `    ``return` `int``(S1 ``+` `S2 ``-` `S3)`` ` `if` `__name__``=``=``'__main__'``:``    ``N ``=` `12``    ``print``(``sum``(N))`` ` `# This code is contributed by Shrikant13`

## C#

 `// C# program to find sum of ``// numbers from 1 to N which ``// are divisible by 3 or 4 ``using` `System;`` ` `class` `GFG``{`` ` `// Function to calculate the sum ``// of numbers divisible by 3 or 4 ``static` `int` `sum(``int` `N) ``{ ``    ``int` `S1, S2, S3; `` ` `    ``S1 = ((N / 3)) * (2 * 3 + ``          ``(N / 3 - 1) * 3) / 2; ``    ``S2 = ((N / 4)) * (2 * 4 + ``          ``(N / 4 - 1) * 4) / 2; ``    ``S3 = ((N / 12)) * (2 * 12 + ``          ``(N / 12 - 1) * 12) / 2; `` ` `    ``return` `S1 + S2 - S3; ``} `` ` `// Driver code ``public` `static` `void` `Main () ``{``    ``int` `N = 20; `` ` `    ``Console.WriteLine(sum(12)); ``}``} `` ` `// This code is contributed``// by inder_verma`

## PHP

 ``
Output:
```42
```

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