Given an array **A[]** of size **N** and a positive integer **K**, the task is to find the length of the longest subarray such that all elements of the subarray is a factor of **K**.

**Examples:**

Input:A[] = {2, 8, 3, 10, 6, 7, 4, 9}, K = 60Output:3Explanation:The longest subarray in which all elements are a factor of K (= 60) is {3, 10, 6}. Therefore, the required output is 3.

Input:A[] = {7, 20, 8, 10, 5}, K = 20Output:2Explanation:The longest subarray in which all elements are a factor of K (= 20) is {10, 5}. Therefore, the required output is 2.

**Naive Approach:** This simplest approach to solve this problem is to traverse the array and generate all possible subarrays of the given array. For each subarray, check if all its elements are a factor of **K** or not. If found to be true, then store the length of the subarray if it the maximum obtained till then. Finally, print the maximum length obtained as the required answer.

**Time Complexity:** O(N^{3})**Auxiliary Space:** O(1)

**Efficient Approach:** To optimize the above approach, the idea is to traverse the array and check if **arr[i]** is a factor of **K** or not. If found to be true, then increment the length of the subarray. Otherwise, store the length of the subarray if it is the maximum obtained so far and reset to **0**. Follow the steps below to solve the problem:

- Initialize a variable, say
**MaxLen**, to store the length of longest subarray such that every element in the subarray is a factor of**K**. - Initialize a variable, say
**Len**, to store the length of the current subarray. - Traverse the array and check if
**K % arr[i] = 0**or not. If found to be true, then increment the value of**Len**and update the value of**MaxLen = max(Len, MaxLen).** - Finally, print the value of
**MaxLen**.

Below is the implementation of the above approach:

## C++

`// C++ program to implement` `// the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the length of the longest` `// subarray in which all elements are a factor of K` `int` `find_longest_subarray(` `int` `A[], ` `int` `N, ` `int` `K)` `{` ` ` `// Stores length of the longest subarray` ` ` `// in which all elements are a factor of K` ` ` `int` `MaxLen = 0;` ` ` `// Stores length of` ` ` `// the current subarray` ` ` `int` `Len = 0;` ` ` `// Traverse the array arr[]` ` ` `for` `(` `int` `i = 0; i < N; i++) {` ` ` `// If A[i] is a factor of K` ` ` `if` `(K % A[i] == 0) {` ` ` `// Update Len` ` ` `Len++;` ` ` `// Update MaxLen` ` ` `MaxLen = max(MaxLen, Len);` ` ` `}` ` ` `else` `{` ` ` `// Reset Len` ` ` `Len = 0;` ` ` `}` ` ` `}` ` ` `return` `MaxLen;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `A[] = { 2, 8, 3, 10, 6, 7, 4, 9 };` ` ` `int` `N = ` `sizeof` `(A) / ` `sizeof` `(A[0]);` ` ` `;` ` ` `int` `K = 60;` ` ` `cout << find_longest_subarray(A, N, K);` ` ` `return` `0;` `}` |

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## Java

`// Java program to implement` `// the above approach` `import` `java.util.*;` `class` `GFG {` ` ` `// Function to find the length of the longest` ` ` `// subarray in which all elements are a factor of K` ` ` `static` `int` `find_longest_subarray(` `int` `[] A, ` `int` `N,` ` ` `int` `K)` ` ` `{` ` ` `// Stores length of the longest subarray` ` ` `// in which all elements are a factor of K` ` ` `int` `MaxLen = ` `0` `;` ` ` `// Stores length of` ` ` `// the current subarray` ` ` `int` `Len = ` `0` `;` ` ` `// Traverse the array arr[]` ` ` `for` `(` `int` `i = ` `0` `; i < N; i++) {` ` ` `// If A[i] is a` ` ` `// factor of K` ` ` `if` `(K % A[i] == ` `0` `) {` ` ` `// Update Len` ` ` `Len++;` ` ` `// Update MaxLen` ` ` `MaxLen = Math.max(` ` ` `MaxLen, Len);` ` ` `}` ` ` `// If A[i] is not a` ` ` `// factor of K` ` ` `else` `{` ` ` `// Update Len` ` ` `Len = ` `0` `;` ` ` `}` ` ` `}` ` ` `return` `MaxLen;` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `[] A = { ` `2` `, ` `8` `, ` `3` `, ` `10` `, ` `6` `, ` `7` `, ` `4` `, ` `9` `};` ` ` `int` `N = A.length;` ` ` `int` `K = ` `60` `;` ` ` `System.out.println(` ` ` `find_longest_subarray(A, N, K));` ` ` `}` `}` |

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## Python3

`# Python3 program to implement` `# the above approach` ` ` `# Function to find the length of the` `# longest subarray in which all ` `# elements are a factor of K` `def` `find_longest_subarray(A, N, K):` ` ` ` ` `# Stores length of the longest` ` ` `# subarray in which all elements` ` ` `# are a factor of K` ` ` `MaxLen ` `=` `0` ` ` ` ` `# Stores length of the ` ` ` `# current subarray` ` ` `Len` `=` `0` ` ` ` ` `# Traverse the array arr[]` ` ` `for` `i ` `in` `range` `(N):` ` ` ` ` `# If A[i] is a factor of K` ` ` `if` `(K ` `%` `A[i] ` `=` `=` `0` `):` ` ` ` ` `# Update Len` ` ` `Len` `+` `=` `1` ` ` ` ` `# Update MaxLen` ` ` `MaxLen ` `=` `max` `(MaxLen, ` `Len` `)` ` ` ` ` `# If A[i] is not a` ` ` `# factor of K ` ` ` `else` `:` ` ` ` ` `# Reset Len` ` ` `Len` `=` `0` ` ` ` ` `return` `MaxLen` `# Driver Code` `A ` `=` `[ ` `2` `, ` `8` `, ` `3` `, ` `10` `, ` `6` `, ` `7` `, ` `4` `, ` `9` `]` `N ` `=` `len` `(A)` ` ` `K ` `=` `60` ` ` `print` `(find_longest_subarray(A, N, K))` ` ` `# This code is contributed by susmitakundugoaldanga` |

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## C#

`// C# program to implement` `// the above approach` `using` `System;` `class` `GFG{` `// Function to find the length of the longest` `// subarray in which all elements are a factor of K` `static` `int` `find_longest_subarray(` `int` `[] A, ` `int` `N,` ` ` `int` `K)` `{` ` ` ` ` `// Stores length of the longest subarray` ` ` `// in which all elements are a factor of K` ` ` `int` `MaxLen = 0;` ` ` `// Stores length of` ` ` `// the current subarray` ` ` `int` `Len = 0;` ` ` `// Traverse the array arr[]` ` ` `for` `(` `int` `i = 0; i < N; i++)` ` ` `{` ` ` ` ` `// If A[i] is a` ` ` `// factor of K` ` ` `if` `(K % A[i] == 0) ` ` ` `{` ` ` ` ` `// Update Len` ` ` `Len++;` ` ` `// Update MaxLen` ` ` `MaxLen = Math.Max(MaxLen, Len);` ` ` `}` ` ` `// If A[i] is not a` ` ` `// factor of K` ` ` `else` ` ` `{` ` ` ` ` `// Update Len` ` ` `Len = 0;` ` ` `}` ` ` `}` ` ` `return` `MaxLen;` `}` `// Driver Code` `public` `static` `void` `Main(` `string` `[] args)` `{` ` ` `int` `[] A = { 2, 8, 3, 10, 6, 7, 4, 9 };` ` ` `int` `N = A.Length;` ` ` `int` `K = 60;` ` ` ` ` `Console.WriteLine(find_longest_subarray(` ` ` `A, N, K));` `}` `}` `// This code is contributed by chitranayal` |

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**Output:**

3

**Time Complexity:** O(N)**Auxiliary Space:** O(1)

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