# Count numbers in range 1 to N which are divisible by X but not by Y

Given two positive integers X and Y, the task is to count the total numbers in range 1 to N which are divisible by X but not Y.

Examples:

Input: x = 2, Y = 3, N = 10
Output: 4
Numbers divisible by 2 but not 3 are : 2, 4, 8, 10

Input : X = 2, Y = 4, N = 20
Output : 5
Numbers divisible by 2 but not 4 are : 2, 6, 10, 14, 18

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

A Simple Solution is to count numbers divisible by X but not Y is to loop through 1 to N and counting such number which is divisible by X but not Y.

Approach

1. For every number in range 1 to N, Increment count if the number is divisible by X but not by Y.
2. Print the count.
1. Below is the implementation of above approach:

## C++

 `// C++ implementation of above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to count total numbers divisible by ` `// x but not y in range 1 to N ` `int` `countNumbers(``int` `X, ``int` `Y, ``int` `N) ` `{ ` `    ``int` `count = 0; ` `    ``for` `(``int` `i = 1; i <= N; i++) { ` `        ``// Check if Number is divisible ` `        ``// by x but not Y ` `        ``// if yes, Increment count ` `        ``if` `((i % X == 0) && (i % Y != 0)) ` `            ``count++; ` `    ``} ` `    ``return` `count; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` ` `  `    ``int` `X = 2, Y = 3, N = 10; ` `    ``cout << countNumbers(X, Y, N); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation of above approach ` ` `  `class` `GFG { ` ` `  `    ``// Function to count total numbers divisible by ` `    ``// x but not y in range 1 to N ` `    ``static` `int` `countNumbers(``int` `X, ``int` `Y, ``int` `N) ` `    ``{ ` `        ``int` `count = ``0``; ` `        ``for` `(``int` `i = ``1``; i <= N; i++) { ` `            ``// Check if Number is divisible ` `            ``// by x but not Y ` `            ``// if yes, Increment count ` `            ``if` `((i % X == ``0``) && (i % Y != ``0``)) ` `                ``count++; ` `        ``} ` `        ``return` `count; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` ` `  `        ``int` `X = ``2``, Y = ``3``, N = ``10``; ` `        ``System.out.println(countNumbers(X, Y, N)); ` `    ``} ` `} `

## Python3

 `# Python3 implementation of above approach  ` ` `  `# Function to count total numbers divisible  ` `# by x but not y in range 1 to N  ` `def` `countNumbers(X, Y, N):  ` ` `  `    ``count ``=` `0``;  ` `    ``for` `i ``in` `range``(``1``, N ``+` `1``): ` `         `  `        ``# Check if Number is divisible  ` `        ``# by x but not Y  ` `        ``# if yes, Increment count  ` `        ``if` `((i ``%` `X ``=``=` `0``) ``and` `(i ``%` `Y !``=` `0``)):  ` `            ``count ``+``=` `1``;  ` ` `  `    ``return` `count;  ` ` `  `# Driver Code  ` `X ``=` `2``; ` `Y ``=` `3``; ` `N ``=` `10``;  ` `print``(countNumbers(X, Y, N));  ` `     `  `# This code is contributed by mits `

## C#

 `// C# implementation of the above approach ` `using` `System; ` `class` `GFG { ` ` `  `    ``// Function to count total numbers divisible by ` `    ``// x but not y in range 1 to N ` `    ``static` `int` `countNumbers(``int` `X, ``int` `Y, ``int` `N) ` `    ``{ ` `        ``int` `count = 0; ` `        ``for` `(``int` `i = 1; i <= N; i++) { ` `            ``// Check if Number is divisible ` `            ``// by x but not Y ` `            ``// if yes, Increment count ` `            ``if` `((i % X == 0) && (i % Y != 0)) ` `                ``count++; ` `        ``} ` `        ``return` `count; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` ` `  `        ``int` `X = 2, Y = 3, N = 10; ` `        ``Console.WriteLine(countNumbers(X, Y, N)); ` `    ``} ` `} `

## PHP

 ` `

Output:

```4
```

Time Complexity : O(N)

Efficient solution:

1. In range 1 to N, find total numbers divisible by X and total numbers divisible by Y.
2. Also, Find total numbers divisible by either X or Y
3. Calculate total number divisible by X but not Y as
(total number divisible by X or Y) – (total number divisible by Y)

Below is the implementation of above approach:

## C++

 `// C++ implementation of above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to count total numbers divisible by ` `// x but not y in range 1 to N ` `int` `countNumbers(``int` `X, ``int` `Y, ``int` `N) ` `{ ` ` `  `    ``// Count total number divisible by X ` `    ``int` `divisibleByX = N / X; ` ` `  `    ``// Count total number divisible by Y ` `    ``int` `divisibleByY = N / Y; ` ` `  `    ``// Count total number divisible by either X or Y ` `    ``int` `LCM = (X * Y) / __gcd(X, Y); ` `    ``int` `divisibleByLCM = N / LCM; ` `    ``int` `divisibleByXorY = divisibleByX + divisibleByY  ` `                                     ``- divisibleByLCM; ` ` `  `    ``// Count total numbers divisible by X but not Y ` `    ``int` `divisibleByXnotY = divisibleByXorY  ` `                                       ``- divisibleByY; ` ` `  `    ``return` `divisibleByXnotY; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` ` `  `    ``int` `X = 2, Y = 3, N = 10; ` `    ``cout << countNumbers(X, Y, N); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation of above approach ` ` `  `class` `GFG { ` ` `  `    ``// Function to calculate GCD ` ` `  `    ``static` `int` `gcd(``int` `a, ``int` `b) ` `    ``{ ` `        ``if` `(b == ``0``) ` `            ``return` `a; ` `        ``return` `gcd(b, a % b); ` `    ``} ` ` `  `    ``// Function to count total numbers divisible by ` `    ``// x but not y in range 1 to N ` ` `  `    ``static` `int` `countNumbers(``int` `X, ``int` `Y, ``int` `N) ` `    ``{ ` ` `  `        ``// Count total number divisible by X ` `        ``int` `divisibleByX = N / X; ` ` `  `        ``// Count total number divisible by Y ` `        ``int` `divisibleByY = N / Y; ` ` `  `        ``// Count total number divisible by either X or Y ` `        ``int` `LCM = (X * Y) / gcd(X, Y); ` `        ``int` `divisibleByLCM = N / LCM; ` `        ``int` `divisibleByXorY = divisibleByX + divisibleByY ` `                              ``- divisibleByLCM; ` ` `  `        ``// Count total number divisible by X but not Y ` `        ``int` `divisibleByXnotY = divisibleByXorY  ` `                                          ``- divisibleByY; ` ` `  `        ``return` `divisibleByXnotY; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` ` `  `        ``int` `X = ``2``, Y = ``3``, N = ``10``; ` `        ``System.out.println(countNumbers(X, Y, N)); ` `    ``} ` `} `

## Python3

 `# Python 3 implementation of above approach ` `from` `math ``import` `gcd ` ` `  `# Function to count total numbers divisible  ` `# by x but not y in range 1 to N ` `def` `countNumbers(X, Y, N): ` `     `  `    ``# Count total number divisible by X ` `    ``divisibleByX ``=` `int``(N ``/` `X) ` ` `  `    ``# Count total number divisible by Y ` `    ``divisibleByY ``=` `int``(N ``/` `Y) ` ` `  `    ``# Count total number divisible  ` `    ``# by either X or Y ` `    ``LCM ``=` `int``((X ``*` `Y) ``/` `gcd(X, Y)) ` `    ``divisibleByLCM ``=` `int``(N ``/` `LCM) ` `    ``divisibleByXorY ``=` `(divisibleByX ``+`  `                       ``divisibleByY ``-`  `                       ``divisibleByLCM) ` ` `  `    ``# Count total numbers divisible by  ` `    ``# X but not Y ` `    ``divisibleByXnotY ``=` `(divisibleByXorY ``-`  `                        ``divisibleByY) ` ` `  `    ``return` `divisibleByXnotY ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``X ``=` `2` `    ``Y ``=` `3` `    ``N ``=` `10` `    ``print``(countNumbers(X, Y, N)) ` ` `  `# This code is contributed by ` `# Surendra_Gangwar `

## C#

 `// C# implementation of above approach ` ` `  `using` `System; ` `class` `GFG { ` ` `  `    ``// Function to calculate GCD ` `    ``static` `int` `gcd(``int` `a, ``int` `b) ` `    ``{ ` `        ``if` `(b == 0) ` `            ``return` `a; ` `        ``return` `gcd(b, a % b); ` `    ``} ` ` `  `    ``// Function to count total numbers divisible by ` `    ``// x but not y in range 1 to N ` `    ``static` `int` `countNumbers(``int` `X, ``int` `Y, ``int` `N) ` `    ``{ ` ` `  `        ``// Count total number divisible by X ` `        ``int` `divisibleByX = N / X; ` ` `  `        ``// Count total number divisible by Y ` `        ``int` `divisibleByY = N / Y; ` ` `  `        ``// Count total number divisible by either X or Y ` `        ``int` `LCM = (X * Y) / gcd(X, Y); ` `        ``int` `divisibleByLCM = N / LCM; ` `        ``int` `divisibleByXorY = divisibleByX + divisibleByY  ` `                                        ``- divisibleByLCM; ` ` `  `        ``// Count total number divisible by X but not Y ` `        ``int` `divisibleByXnotY = divisibleByXorY  ` `                                          ``- divisibleByY; ` ` `  `        ``return` `divisibleByXnotY; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` ` `  `        ``int` `X = 2, Y = 3, N = 10; ` `        ``Console.WriteLine(countNumbers(X, Y, N)); ` `    ``} ` `} `

## PHP

 ` ``\$b``)  ` `        ``return` `__gcd( ``\$a` `- ``\$b` `, ``\$b` `);  ` ` `  `    ``return` `__gcd( ``\$a` `, ``\$b` `- ``\$a` `);  ` `}  ` ` `  `// Function to count total numbers divisible  ` `// by x but not y in range 1 to N ` `function` `countNumbers(``\$X``, ``\$Y``, ``\$N``) ` `{ ` ` `  `    ``// Count total number divisible by X ` `    ``\$divisibleByX` `= ``\$N` `/ ``\$X``; ` ` `  `    ``// Count total number divisible by Y ` `    ``\$divisibleByY` `= ``\$N` `/``\$Y``; ` ` `  `    ``// Count total number divisible by either X or Y ` `    ``\$LCM` `= (``\$X` `* ``\$Y``) / __gcd(``\$X``, ``\$Y``); ` `    ``\$divisibleByLCM` `= ``\$N` `/ ``\$LCM``; ` `    ``\$divisibleByXorY` `= ``\$divisibleByX` `+ ``\$divisibleByY` `-  ` `                                       ``\$divisibleByLCM``; ` ` `  `    ``// Count total numbers divisible by X but not Y ` `    ``\$divisibleByXnotY` `= ``\$divisibleByXorY` `-  ` `                        ``\$divisibleByY``; ` ` `  `    ``return` `ceil``(``\$divisibleByXnotY``); ` `} ` ` `  `// Driver Code ` `\$X` `= 2; ` `\$Y` `= 3; ` `\$N` `= 10; ` `echo` `countNumbers(``\$X``, ``\$Y``, ``\$N``); ` ` `  `// This is code contrubted by inder_verma ` `?> `

Output:

```4
```

Time Complexity: O(1)

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