# Longest sub-sequence with maximum GCD

• Last Updated : 12 May, 2021

Given an array arr[] of length N, the task is to find the length of the longest sub-sequence with the maximum possible GCD.
Examples:

Input: arr[] = {2, 1, 2}
Output:
{2}, {2} and {2, 2} are the subsequences
with the maximum possible GCD.
Input: arr[] = {1, 2, 3}
Output:
{3} is the required subsequence.

Approach: The maximum possible GCD from the array will be equal to the value of the largest element in the array. Now, to maximize the length of the resulting subsequence, find the number of elements with a value equal to this largest value in the array, and the count of these elements is the required answer.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the length``// of the largest subsequence with``// maximum possible GCD``int` `maxLen(``int``* arr, ``int` `n)``{``    ``// Maximum value from the array``    ``int` `max_val = *max_element(arr, arr + n);` `    ``// To store the frequency of the``    ``// maximum element in the array``    ``int` `freq = 0;` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``// If current element is equal``        ``// to the maximum element``        ``if` `(arr[i] == max_val)``            ``freq++;``    ``}` `    ``return` `freq;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 3, 2, 2, 3, 3, 3 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);` `    ``cout << maxLen(arr, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``import` `java.util.Arrays;` `class` `GFG``{` `// Function to return the length``// of the largest subsequence with``// maximum possible GCD``static` `int` `maxLen(``int``[] arr, ``int` `n)``{``    ``// Maximum value from the array``    ``int` `max_val = Arrays.stream(arr).max().getAsInt();` `    ``// To store the frequency of the``    ``// maximum element in the array``    ``int` `freq = ``0``;` `    ``for` `(``int` `i = ``0``; i < n; i++)``    ``{` `        ``// If current element is equal``        ``// to the maximum element``        ``if` `(arr[i] == max_val)``            ``freq++;``    ``}``    ``return` `freq;``}` `// Driver code``public` `static` `void` `main(String []args)``{``    ``int` `arr[] = { ``3``, ``2``, ``2``, ``3``, ``3``, ``3` `};``    ``int` `n = arr.length;` `    ``System.out.println(maxLen(arr, n));``}``}` `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach` `# Function to return the length``# of the largest subsequence with``# maximum possible GCD``def` `maxLen(arr, n) :``    ` `    ``# Maximum value from the array``    ``max_val ``=` `max``(arr);` `    ``# To store the frequency of the``    ``# maximum element in the array``    ``freq ``=` `0``;` `    ``for` `i ``in` `range``(n) :` `        ``# If current element is equal``        ``# to the maximum element``        ``if` `(arr[i] ``=``=` `max_val) :``            ``freq ``+``=` `1``;` `    ``return` `freq;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``arr ``=` `[ ``3``, ``2``, ``2``, ``3``, ``3``, ``3` `];``    ``n ``=` `len``(arr);` `    ``print``(maxLen(arr, n));` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;``using` `System.Linq;` `class` `GFG``{` `// Function to return the length``// of the largest subsequence with``// maximum possible GCD``static` `int` `maxLen(``int``[] arr, ``int` `n)``{``    ``// Maximum value from the array``    ``int` `max_val = arr.Max();` `    ``// To store the frequency of the``    ``// maximum element in the array``    ``int` `freq = 0;` `    ``for` `(``int` `i = 0; i < n; i++)``    ``{` `        ``// If current element is equal``        ``// to the maximum element``        ``if` `(arr[i] == max_val)``            ``freq++;``    ``}``    ``return` `freq;``}` `// Driver code``public` `static` `void` `Main(String []args)``{``    ``int` `[]arr = { 3, 2, 2, 3, 3, 3 };``    ``int` `n = arr.Length;` `    ``Console.WriteLine(maxLen(arr, n));``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``
Output:
`4`

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