Problem Solving

If n=4p, where p is prime number greater than 2, how many different positive even divisors does n have, including n ?

A) 2
B) 3
C) 4
D) 6
E) 8

Interested in learning the DIFFERENT approaches to solve this problem. Ultimately in the best and quickest approach.

My approach:
whenever I see the following words or terms in a question: "prime" and "divisors", I automatically start to think about breaking a number down into its prime factors which are the foundation for all the numbers.
So n = 4p.
Ok ... so 4p has the following prime factors: 2, 2, p.
"p is prime number greater than 2" - this statement is telling us that p CANNOT be even since 2 is the only even prime number. I dont know why they placed this "greater than 2" statement into the question. Is this a trap ... were GMAT trying to trip us up ... when eventually asking us to fine the possible "even divisors" of n.

Ok ... so we know n=4p ... 4p has the following prime factors: 2, 2, p.
So 4p has the following factors: 2, 2p, 4, 4p.
"how many different positive EVEN divisors does n have ?" well we know anything multiplied by an even number will always be even ... so even though p is a prime number greater than 2 (in other words odd) ... 2p and 4p will always be even.
So we can say that n has 4 positive even factors (or divisors), including n (n=4p).

Any other approaches/strategies to tackle this question. Any spot any other traps/tricks here ?

Thanks.