5

Max GCD Pair

Difficulty: MEDIUM
Contributed By
Sounak Majumder
Avg. time to solve
35 min
Success Rate
75%

Problem Statement

You are given an array of positive integers. Find the GCD(Greatest Common Divisor) of a pair of elements such that it is maximum among all possible pairs. GCD(a, b) is the maximum number x such that both a and b are divisible by x.

For example: 
If the given array is {1, 5, 2, 3, 4}, the output will be 2 (which is GCD of 2 and 4, all other pairs have a GCD of 1)
Input format :
The first line of input contains a single integer 'T', representing the number of test cases or queries to be run. 
Then the 'T' test cases follow.

The first line of each test case contains a positive integer 'N', which represents the size of the array.

The next line contains 'N' single space-separated positive integers representing the elements of the array.
Output Format :
For each test case, print a single line containing a single integer denoting the maximum GCD value.

The output of each test case will be printed in a separate line.
Note:
You do not need to print anything, it has already been taken care of. Just implement the given function.
Constraints :
1 <= T <= 10
2 <= N <= 10 ^ 4
1 <= ARR[i] <= 10 ^ 5

Where 'T' is the number of test cases, 'N' is the size of the array and ARR[i] is the ith element in the array.

Time Limit: 1 sec.
Sample Input 1:
3
5
5 2 4 3 1
5
2 4 6 5 6
10
4 2 10 8 6 4 3 2 1 7
Sample Output 1:
2
6
4
Explanation for Sample Input 1:
In the 1st test case, pair (2,4) has a maximum GCD value of 2, all other pairs have a GCD of 1.

In the 2nd test case, pair (6,6) has a maximum GCD value of 6, all other pairs have GCD less than 6.

In the 3rd test case, pair (4,8) has a maximum GCD value of 4, all other pairs have GCD less than 4. 
Sample Input 2:
2
4
2 4 6 8 
5
1 2 3 4 5
Sample Output 2:
4
2
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