Max GCD Pair

Moderate

0/80

Average time to solve is 35m

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13 upvotes

Asked in companies

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)

Detailed explanation ( Input/output format, Notes, Images )

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:

Sample Output 2:

4
2

Console