#### Recently I found one amazing problem on Hackerearth that seems to be difficult to be solved within time limits.

we are given an array A of n positive integers and we are supposed to calculate **MGCD**(k) of A. Here **MGCD**(k) is the Modified GCD of Order K for an Array A.

Modified GCD of Order K for an array is the Maximum number that divides at least **ceil**(n/k) number of elements of the array.For example Modified Gcd of Order 2 for array A is the Maximum number that divides at least half of its elements. For example-given n=10, k=3 and array A={24 18 28 8 25 1 48 27 56 16}

In the above example 8 divides 5 elements of the array(24,8,48,56,16) ,which is greater than(>=) **ceil**(10/3) i.e.=4 There is no number greater 8 than that divides at least 4 numbers of the array.So 8 is the required answer.

The problem is https://www.hackerearth.com/ru/problem/algorithm/modified-gcd/, right?

yes exactly but I am not able to digest the solution provided there in the editorial

If a number $$$d$$$ divides a number $$$n$$$, then any of its prime factors will do as well. So why not factorize every number in the array and store how many elements each primes divides by using a map?

but factorization itself will take square root of A[i] time where A[i] i.e. the elements are of order

10^12and that will lead to TLE beauuse at the same time we have to processn=10^5. So we need to do look for an algorithm that runs in O(n).Help if someone gets the logicIndeed.

Just like the editorial says, since K is very small, we can use a randomized solution. Pick an element, factorize it and check if divisors divide required number of elements.

Keep the maximum element you find.

ya You are right I think that is the only possible solution to this problem. But I came here in hope of some other possible solution!!