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# Count integers in the range [A, B] that are not divisible by C and D

• Difficulty Level : Basic
• Last Updated : 27 Apr, 2021

Given four integers A, B, C and D. The task is to find the count of integers in the range [A, B] that are not divisible by C and D .
Examples:

Input: A = 4, B = 9, C = 2, D = 3
Output:
5 and 7 are such integers.
Input: A = 10, B = 50, C = 4, D = 6
Output: 28

Approach: First include all the integers in the range in the required answer i.e. B – A + 1. Then remove all the numbers which are divisible by C and D and finally add all the numbers which are divisible by both C and D.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the count of``// integers from the range [a, b] that``// are not divisible by c and d``int` `countNums(``int` `a, ``int` `b, ``int` `c, ``int` `d)``{``    ``// Numbers which are divisible by c``    ``int` `x = b / c - (a - 1) / c;` `    ``// Numbers which are divisible by d``    ``int` `y = b / d - (a - 1) / d;` `    ``// Find lowest common factor of c and d``    ``int` `k = (c * d) / __gcd(c, d);` `    ``// Numbers which are divisible by both c and d``    ``int` `z = b / k - (a - 1) / k;` `    ``// Return the required answer``    ``return` `b - a + 1 - x - y + z;``}` `// Driver code``int` `main()``{``    ``int` `a = 10, b = 50, c = 4, d = 6;` `    ``cout << countNums(a, b, c, d);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{` `// Function to return the count of``// integers from the range [a, b] that``// are not divisible by c and d``static` `int` `countNums(``int` `a, ``int` `b, ``int` `c, ``int` `d)``{``    ``// Numbers which are divisible by c``    ``int` `x = b / c - (a - ``1``) / c;` `    ``// Numbers which are divisible by d``    ``int` `y = b / d - (a - ``1``) / d;` `    ``// Find lowest common factor of c and d``    ``int` `k = (c * d) / __gcd(c, d);` `    ``// Numbers which are divisible by both c and d``    ``int` `z = b / k - (a - ``1``) / k;` `    ``// Return the required answer``    ``return` `b - a + ``1` `- x - y + z;``}``static` `int` `__gcd(``int` `a, ``int` `b)``{``    ``if` `(b == ``0``)``        ``return` `a;``    ``return` `__gcd(b, a % b);    ``}` `// Driver code``public` `static` `void` `main(String []args)``{``    ``int` `a = ``10``, b = ``50``, c = ``4``, d = ``6``;` `    ``System.out.println(countNums(a, b, c, d));``}``}` `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 implementation of the approach``from` `math ``import` `gcd` `# Function to return the count of``# integers from the range [a, b] that``# are not divisible by c and d``def` `countNums(a, b, c, d) :` `    ``# Numbers which are divisible by c``    ``x ``=` `b ``/``/` `c ``-` `(a ``-` `1``) ``/``/` `c;` `    ``# Numbers which are divisible by d``    ``y ``=` `b ``/``/` `d ``-` `(a ``-` `1``) ``/``/` `d;` `    ``# Find lowest common factor of c and d``    ``k ``=` `(c ``*` `d) ``/``/` `gcd(c, d);` `    ``# Numbers which are divisible``    ``# by both c and d``    ``z ``=` `b ``/``/` `k ``-` `(a ``-` `1``) ``/``/` `k;` `    ``# Return the required answer``    ``return` `(b ``-` `a ``+` `1` `-` `x ``-` `y ``+` `z);` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``a ``=` `10``; b ``=` `50``; c ``=` `4``; d ``=` `6``;` `    ``print``(countNums(a, b, c, d));` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;``    ` `class` `GFG``{` `// Function to return the count of``// integers from the range [a, b] that``// are not divisible by c and d``static` `int` `countNums(``int` `a, ``int` `b, ``int` `c, ``int` `d)``{``    ``// Numbers which are divisible by c``    ``int` `x = b / c - (a - 1) / c;` `    ``// Numbers which are divisible by d``    ``int` `y = b / d - (a - 1) / d;` `    ``// Find lowest common factor of c and d``    ``int` `k = (c * d) / __gcd(c, d);` `    ``// Numbers which are divisible by both c and d``    ``int` `z = b / k - (a - 1) / k;` `    ``// Return the required answer``    ``return` `b - a + 1 - x - y + z;``}` `static` `int` `__gcd(``int` `a, ``int` `b)``{``    ``if` `(b == 0)``        ``return` `a;``    ``return` `__gcd(b, a % b);    ``}` `// Driver code``public` `static` `void` `Main(String []args)``{``    ``int` `a = 10, b = 50, c = 4, d = 6;` `    ``Console.WriteLine(countNums(a, b, c, d));``}``}` `// This code is contributed by Rajput-Ji`

## Javascript

 ``
Output:
`28`

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