Simple O(n) Solution in Java
Code

# Code
```java []
class Solution {
    public int maxDivScore(int[] nums, int[] divisors) {
        int maxSoFar = 0;
        int divisor = Integer.MAX_VALUE;

        for(int i=0;i<divisors.length;i++){
            int count = 0;
            for(int j=0;j<nums.length;j++){
                if(nums[j]%divisors[i] == 0)count++;
            }
            if(count > maxSoFar || (count == maxSoFar && divisors[i] < divisor)){
                maxSoFar = count;
                divisor = divisors[i];
            }
        }

        return divisor;
    }
}
```
['Array', 'Java']