# Count of numbers upto M divisible by given Prime Numbers

Given an array **arr[]** of Prime Numbers and a number **M**, the task is to count the number of elements in the range **[1, M]** that are divisible by any of the given prime numbers.

**Examples:**

Input:arr[] = {2, 3, 5, 7} M = 100Output:78Explanation:

In total there are 78 numbers that are divisible by either of 2 3 5 or 7.

Input:arr[] = {2, 5, 7, 11} M = 200Output:137Explanation:

In total there are 137 numbers that are divisible by either of 2 5 7 or 11.

**Naive Approach:** The idea is iterate over the range **[1, M]** and check if any of the array element is divides the element in the range **[1, M]** then count the element else check for the next number in the range.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <iostream>` `using` `namespace` `std;` `// Function to count the numbers that` `// are divisible by the numbers in` `// the array from range 1 to M` `int` `count(` `int` `a[], ` `int` `M, ` `int` `N)` `{` ` ` `// Initialize the count variable` ` ` `int` `cnt = 0;` ` ` `// Iterate over [1, M]` ` ` `for` `(` `int` `i = 1; i <= M; i++) {` ` ` `// Iterate over array elements arr[]` ` ` `for` `(` `int` `j = 0; j < N; j++) {` ` ` `// Check if i is divisible by a[j]` ` ` `if` `(i % a[j] == 0) {` ` ` `// Increment the count` ` ` `cnt++;` ` ` `break` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `// Return the answer` ` ` `return` `cnt;` `}` `// Driver code` `int` `main()` `{` ` ` `// Given array arr[]` ` ` `int` `arr[] = { 2, 3, 5, 7 };` ` ` `// Given Number M` ` ` `int` `m = 100;` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` `// Function Call` ` ` `cout << count(arr, m, n);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `class` `GFG{` `// Function to count the numbers that` `// are divisible by the numbers in` `// the array from range 1 to M` `static` `int` `count(` `int` `a[], ` `int` `M, ` `int` `N)` `{` ` ` ` ` `// Initialize the count variable` ` ` `int` `cnt = ` `0` `;` ` ` `// Iterate over [1, M]` ` ` `for` `(` `int` `i = ` `1` `; i <= M; i++)` ` ` `{` ` ` ` ` `// Iterate over array elements arr[]` ` ` `for` `(` `int` `j = ` `0` `; j < N; j++)` ` ` `{` ` ` ` ` `// Check if i is divisible by a[j]` ` ` `if` `(i % a[j] == ` `0` `)` ` ` `{` ` ` ` ` `// Increment the count` ` ` `cnt++;` ` ` `break` `;` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// Return the answer` ` ` `return` `cnt;` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Given array arr[]` ` ` `int` `arr[] = { ` `2` `, ` `3` `, ` `5` `, ` `7` `};` ` ` `// Given number M` ` ` `int` `m = ` `100` `;` ` ` `int` `n = arr.length;` ` ` `// Function call` ` ` `System.out.print(count(arr, m, n));` `}` `}` `// This code is contributed by Amit Katiyar` |

## Python3

`# Python3 program for the above approach` `# Function to count the numbers that` `# are divisible by the numbers in` `# the array from range 1 to M` `def` `count(a, M, N):` ` ` ` ` `# Initialize the count variable` ` ` `cnt ` `=` `0` ` ` `# Iterate over [1, M]` ` ` `for` `i ` `in` `range` `(` `1` `, M ` `+` `1` `):` ` ` `# Iterate over array elements arr[]` ` ` `for` `j ` `in` `range` `(N):` ` ` `# Check if i is divisible by a[j]` ` ` `if` `(i ` `%` `a[j] ` `=` `=` `0` `):` ` ` `# Increment the count` ` ` `cnt ` `+` `=` `1` ` ` `break` ` ` `# Return the answer` ` ` `return` `cnt` `# Driver code` `# Given list lst` `lst ` `=` `[ ` `2` `, ` `3` `, ` `5` `, ` `7` `]` `# Given number M` `m ` `=` `100` `n ` `=` `len` `(lst)` `# Function call` `print` `(count(lst, m, n))` `# This code is contributed by vishu2908 ` |

## C#

`// C# program for the above approach` `using` `System;` `class` `GFG{` `// Function to count the numbers that` `// are divisible by the numbers in` `// the array from range 1 to M` `static` `int` `count(` `int` `[]a, ` `int` `M, ` `int` `N)` `{` ` ` ` ` `// Initialize the count variable` ` ` `int` `cnt = 0;` ` ` `// Iterate over [1, M]` ` ` `for` `(` `int` `i = 1; i <= M; i++)` ` ` `{` ` ` ` ` `// Iterate over array elements []arr` ` ` `for` `(` `int` `j = 0; j < N; j++)` ` ` `{` ` ` ` ` `// Check if i is divisible by a[j]` ` ` `if` `(i % a[j] == 0)` ` ` `{` ` ` ` ` `// Increment the count` ` ` `cnt++;` ` ` `break` `;` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `// Return the answer` ` ` `return` `cnt;` `}` `// Driver code` `public` `static` `void` `Main(String[] args)` `{` ` ` ` ` `// Given array []arr` ` ` `int` `[]arr = { 2, 3, 5, 7 };` ` ` `// Given number M` ` ` `int` `m = 100;` ` ` `int` `n = arr.Length;` ` ` `// Function call` ` ` `Console.Write(count(arr, m, n));` `}` `}` `// This code is contributed by Amit Katiyar` |

## Javascript

`<script>` ` ` `// Javascript program for the above approach` ` ` ` ` `// Function to count the numbers that` ` ` `// are divisible by the numbers in` ` ` `// the array from range 1 to M` ` ` `function` `count(a, M, N)` ` ` `{` ` ` `// Initialize the count variable` ` ` `let cnt = 0;` ` ` `// Iterate over [1, M]` ` ` `for` `(let i = 1; i <= M; i++) {` ` ` `// Iterate over array elements arr[]` ` ` `for` `(let j = 0; j < N; j++) {` ` ` `// Check if i is divisible by a[j]` ` ` `if` `(i % a[j] == 0) {` ` ` `// Increment the count` ` ` `cnt++;` ` ` `break` `;` ` ` `}` ` ` `}` ` ` `}` ` ` `// Return the answer` ` ` `return` `cnt;` ` ` `}` ` ` ` ` `// Given array arr[]` ` ` `let arr = [ 2, 3, 5, 7 ];` ` ` ` ` `// Given Number M` ` ` `let m = 100;` ` ` `let n = arr.length;` ` ` ` ` `// Function Call` ` ` `document.write(count(arr, m, n));` ` ` `</script>` |

**Output**

78

**Time Complexity:** O(N*M) **Auxiliary Space:** O(1) **Another Approach:** Another method to solve this problem is use Dynamic Programming and Seive. Mark all the numbers up to M that are divisible by any prime number in the array. Then count all the marked numbers and print it.

Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the **Essential Maths for CP Course** at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**