# Count the numbers divisible by ‘M’ in a given range

A and B are two numbers which define a range, where A <= B. Find the total numbers in the given range [A … B] divisible by ‘M’

Examples:

Input : A = 25, B = 100, M = 30 Output : 3 Explanation : In the given range [25 - 100], 30, 60 and 90 are divisible by 30 Input : A = 6, B = 15, M = 3 Output : 4 Explanation : In the given range [6 - 15], 6, 9, 12 and 15 are divisible by 3

**Method 1 : [Brute-force]**

Run a loop from A to B. If a number divisible by ‘M’ is found, increment counter.

Below is the implementation of above method:

## C++

`// Program to count the numbers divisible by` `// M in a given range` `#include <bits/stdc++.h>` `using` `namespace` `std;` `int` `countDivisibles(` `int` `A, ` `int` `B, ` `int` `M)` `{` ` ` `// Variable to store the counter` ` ` `int` `counter = 0;` ` ` `// Running a loop from A to B and check` ` ` `// if a number is divisible by M.` ` ` `for` `(` `int` `i = A; i <= B; i++)` ` ` `if` `(i % M == 0)` ` ` `counter++;` ` ` `return` `counter;` `}` `// Driver code` `int` `main()` `{` ` ` `// A and B define the range, M is the dividend` ` ` `int` `A = 30, B = 100, M = 30;` ` ` `// Printing the result` ` ` `cout << countDivisibles(A, B, M) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to count the numbers divisible by` `// M in a given range` `import` `java.io.*;` `class` `GFG {` ` ` `// Function to count the numbers divisible by` ` ` `// M in a given range` ` ` `static` `int` `countDivisibles(` `int` `A, ` `int` `B, ` `int` `M)` ` ` `{` ` ` `// Variable to store the counter` ` ` `int` `counter = ` `0` `;` ` ` `// Running a loop from A to B and check` ` ` `// if a number is divisible by M.` ` ` `for` `(` `int` `i = A; i <= B; i++)` ` ` `if` `(i % M == ` `0` `)` ` ` `counter++;` ` ` `return` `counter;` ` ` `}` ` ` `// driver program` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// A and B define the range, M is the dividend` ` ` `int` `A = ` `30` `, B = ` `100` `, M = ` `30` `;` ` ` `// Printing the result` ` ` `System.out.println(countDivisibles(A, B, M));` ` ` `}` `}` `// Contributed by Pramod Kumar` |

## Python3

`# Program to count the numbers` `# divisible by M in a given range` `def` `countDivisibles(A, B, M):` ` ` ` ` `# Variable to store the counter` ` ` `counter ` `=` `0` `;` ` ` `# Running a loop from A to B` ` ` `# and check if a number is` ` ` `# divisible by M.` ` ` `for` `i ` `in` `range` `(A, B):` ` ` `if` `(i ` `%` `M ` `=` `=` `0` `):` ` ` `counter ` `=` `counter ` `+` `1` ` ` `return` `counter` `# Driver code` `# A and B define the range,` `# M is the dividend` `A ` `=` `30` `B ` `=` `100` `M ` `=` `30` `# Printing the result` `print` `(countDivisibles(A, B, M))` `# This code is contributed by Sam007.` |

## C#

`// C# program to count the numbers` `// divisible by M in a given range` `using` `System;` `public` `class` `GFG {` ` ` `// Function to count the numbers divisible by` ` ` `// M in a given range` ` ` `static` `int` `countDivisibles(` `int` `A, ` `int` `B, ` `int` `M)` ` ` `{` ` ` `// Variable to store the counter` ` ` `int` `counter = 0;` ` ` `// Running a loop from A to B and check` ` ` `// if a number is divisible by M.` ` ` `for` `(` `int` `i = A; i <= B; i++)` ` ` `if` `(i % M == 0)` ` ` `counter++;` ` ` `return` `counter;` ` ` `}` ` ` `// driver program` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `// A and B define the range, M is the dividend` ` ` `int` `A = 30, B = 100, M = 30;` ` ` `// Printing the result` ` ` `Console.WriteLine(countDivisibles(A, B, M));` ` ` `}` `}` `// This code is contributed by Sam007` |

## PHP

`<?php` `// PHP Program to count the` `// numbers divisible by` `// M in a given range` `function` `countDivisibles(` `$A` `, ` `$B` `, ` `$M` `)` `{` ` ` ` ` `// Variable to store the counter` ` ` `$counter` `= 0;` ` ` `// Running a loop from` ` ` `// A to B and check` ` ` `// if a number is` ` ` `// divisible by M.` ` ` `for` `(` `$i` `= ` `$A` `; ` `$i` `<= ` `$B` `; ` `$i` `++)` ` ` `if` `(` `$i` `% ` `$M` `== 0)` ` ` `$counter` `++;` ` ` `return` `$counter` `;` `}` ` ` `// Driver Code` ` ` `// A and B define the range,` ` ` `// M is the dividend` ` ` `$A` `= 30;` ` ` `$B` `= 100;` ` ` `$M` `= 30;` ` ` `// Printing the result` ` ` `echo` `countDivisibles(` `$A` `, ` `$B` `, ` `$M` `), ` `"\n"` `;` `// This code is contributed by ajit` `?>` |

## Javascript

`<script>` `// Javascript Program to count the` `// numbers divisible by` `// M in a given range` `function` `countDivisibles(A, B, M)` `{` ` ` ` ` `// Variable to store the counter` ` ` `let counter = 0;` ` ` `// Running a loop from` ` ` `// A to B and check` ` ` `// if a number is` ` ` `// divisible by M.` ` ` `for` `(let i = A; i <= B; i++)` ` ` `if` `(i % M == 0)` ` ` `counter++;` ` ` `return` `counter;` `}` ` ` `// Driver Code` ` ` `// A and B define the range,` ` ` `// M is the dividend` ` ` `let A = 30;` ` ` `let B = 100;` ` ` `let M = 30;` ` ` `// Printing the result` ` ` `document.write(countDivisibles(A, B, M));` `// This code is contributed by gfgking.` `</script>` |

Output:

3

**Time Complexity: **O(B)

**Auxiliary Space: **O(1)**Method 2 : [Better]**

The loop can be modified by incrementing the iterator ‘M’ times after the first divisible is found. Also, if ‘A’ is less than ‘M’, it can be changed to ‘M’, because a number less than ‘M’ can not be divided by it.**Method 3 : [Efficient]**

Let B = b * M and A = a * M The count of numbers divisible by 'M' between A and B will be equal to b - a. Example: A = 25, B = 70, M = 10. Now, a = 2, b = 7. Count = 7 - 2 = 5.

It can be observed that, if A is divisible by M, ‘b – a’ will exclude the count for A, so the count will be less by 1. Thus, in this case we add 1 explicitly.**Example when A is divisible by M:**

A = 30, B = 70, M = 10. Now, a = 3, b = 7. Count = 7 - 3 = 4. But, Count should be 5. Thus, we will add 1 explicitly.

Below is the implementation of the above method :

## C++

`// C++ program to count the numbers divisible by` `// M in a given range` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to count the numbers divisible by` `// M in a given range` `int` `countDivisibles(` `int` `A, ` `int` `B, ` `int` `M)` `{` ` ` ` ` `// Add 1 explicitly as A is divisible by M` ` ` `if` `(A % M == 0)` ` ` `return` `(B / M) - (A / M) + 1;` ` ` `// A is not divisible by M` ` ` `return` `(B / M) - (A / M);` `}` `// driver program` `int` `main()` `{` ` ` ` ` `// A and B define the range, M is the dividend` ` ` `int` `A = 30, B = 100, M = 30;` ` ` `// Printing the result` ` ` `cout << (countDivisibles(A, B, M));` `}` `// This code is contributed by subham348.` |

## Java

`// Java program to count the numbers divisible by` `// M in a given range` `import` `java.io.*;` `class` `GFG {` ` ` `// Function to count the numbers divisible by` ` ` `// M in a given range` ` ` `static` `int` `countDivisibles(` `int` `A, ` `int` `B, ` `int` `M)` ` ` `{` ` ` `// Add 1 explicitly as A is divisible by M` ` ` `if` `(A % M == ` `0` `)` ` ` `return` `(B / M) - (A / M) + ` `1` `;` ` ` `// A is not divisible by M` ` ` `return` `(B / M) - (A / M);` ` ` `}` ` ` `// driver program` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `// A and B define the range, M is the dividend` ` ` `int` `A = ` `30` `, B = ` `100` `, M = ` `30` `;` ` ` `// Printing the result` ` ` `System.out.println(countDivisibles(A, B, M));` ` ` `}` `}` `// Contributed by Pramod Kumar` |

## Python3

`# Program to count the numbers divisible` `# by M in a given range` `# Returns count of numbers in [A B] that` `# are divisible by M.` `def` `countDivisibles(A, B, M):` ` ` ` ` `# Add 1 explicitly as A is divisible by M` ` ` `if` `(A ` `%` `M ` `=` `=` `0` `):` ` ` `return` `((B ` `/` `M) ` `-` `(A ` `/` `M)) ` `+` `1` ` ` `# A is not divisible by M` ` ` `return` `((B ` `/` `M) ` `-` `(A ` `/` `M))` `# Driver Code` `# A and B define the range, M` `# is the dividend` `A ` `=` `30` `B ` `=` `70` `M ` `=` `10` `# Printing the result` `print` `(countDivisibles(A, B, M))` `# This code is contributed by Sam007` |

## C#

`// C# program to count the numbers` `// divisible by M in a given range` `using` `System;` `public` `class` `GFG {` ` ` `// Function to count the numbers divisible by` ` ` `// M in a given range` ` ` `static` `int` `countDivisibles(` `int` `A, ` `int` `B, ` `int` `M)` ` ` `{` ` ` `// Add 1 explicitly as A is divisible by M` ` ` `if` `(A % M == 0)` ` ` `return` `(B / M) - (A / M) + 1;` ` ` `// A is not divisible by M` ` ` `return` `(B / M) - (A / M);` ` ` `}` ` ` `// driver program` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `// A and B define the range, M is the dividend` ` ` `int` `A = 30, B = 100, M = 30;` ` ` `// Printing the result` ` ` `Console.WriteLine(countDivisibles(A, B, M));` ` ` `}` `}` `// This code is contributed by Sam007` |

## PHP

`<?php` `// PHP Program to count the numbers` `// divisible by M in a given range` `// Returns count of numbers in` `// [A B] that are divisible by M.` `function` `countDivisibles(` `$A` `, ` `$B` `, ` `$M` `)` `{` ` ` ` ` `// Add 1 explicitly as A` ` ` `// is divisible by M` ` ` `if` `(` `$A` `% ` `$M` `== 0)` ` ` `return` `(` `$B` `/ ` `$M` `) -` ` ` `(` `$A` `/ ` `$M` `) + 1;` ` ` `// A is not divisible by M` ` ` `return` `(` `$B` `/ ` `$M` `) -` ` ` `(` `$A` `/ ` `$M` `);` `}` ` ` `// Driver Code` ` ` `// A and B define the range,` ` ` `// M is the dividend` ` ` `$A` `= 30;` ` ` `$B` `= 70;` ` ` `$M` `= 10;` ` ` `// Printing the result` ` ` `echo` `countDivisibles(` `$A` `, ` `$B` `, ` `$M` `) ;` ` ` `return` `0;` `// This code is contributed by nitin mittal.` `?>` |

## Javascript

`// Javascript Program to count the numbers` `// divisible by M in a given range` `// Returns count of numbers in` `// [A B] that are divisible by M.` `function` `countDivisibles(A, B, M)` `{` ` ` ` ` `// Add 1 explicitly as A` ` ` `// is divisible by M` ` ` `if` `(A % M == 0)` ` ` `return` `(B / M) -` ` ` `(A / M) + 1;` ` ` `// A is not divisible by M` ` ` `return` `(B / M) -` ` ` `(A / M);` `}` ` ` `// Driver Code` ` ` `// A and B define the range,` ` ` `// M is the dividend` ` ` `let A = 30;` ` ` `let B = 70;` ` ` `let M = 10;` ` ` `// Printing the result` ` ` `document.write(countDivisibles(A, B, M));` `// This code is contributed by gfgking` |

**Output**

3

**Time Complexity: **O(1)

**Auxiliary Space: **O(1)

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