# HackerRank ‘Between Two Sets’ Solution

##### Short Problem Definition:

You will be given two arrays of integers and asked to determine all integers that satisfy the following two conditions:

1. The elements of the first array are all factors of the integer being considered
2. The integer being considered is a factor of all elements of the second array

Between Two Sets

##### Complexity:

time complexity is O(A* (N+M))

space complexity is O(1)

##### Execution:

This challenge could also be solved using the Greatest Common Divisor. Given that the range of values is only [1,100], it is safe to assume that the naive solution will terminate within the time limit.

##### Solution:
```#!/bin/python

import sys

def isValid(a, b, candidate):
for a_ele in a:
if candidate % a_ele != 0:
return False
for b_ele in b:
if b_ele % candidate != 0:
return False
return True

n,m = raw_input().strip().split(' ')
n,m = [int(n),int(m)]
a = map(int,raw_input().strip().split(' '))
b = map(int,raw_input().strip().split(' '))

cnt = 0
for candidate in xrange(max(a), min(b)+1):
if isValid(a, b, candidate):
cnt += 1

print cnt
```

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