Explanation

First, list all of the factors of 210. The easiest way to do this is in pairs, starting with 1 and 210 (remember, the number itself is considered one of its factors). Count up from one and check to see if each number you count is a factor of 210.

1 and 210
2 and 105
3 and 70
5 and 42
7 and 3
10 and 21
14 and 15

When you reach 14, you’ll see that you’ll just repeat 15 and 14 if you keep counting, so you know you’re finished. The question asked for the greatest and smallest positive difference between any two factors. (It’s helpful that the question specified positive difference so you know you don’t need to count negative differences, though once you look at the answer choices you can see that’s not what the question is asking for). The way you listed the factors makes this easy because as you look down the list, the difference between factors decreases.

So the greatest difference is between 210 and 1, and the smallest difference is between 14 and 15. The final answer is 209 and 1.

Hence option E is correct.