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; ` `}` |

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## 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 ` |

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## 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 ` |

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**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.

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