I hope the above image is visible. Now here we are saying that n has to be atleast (2^2)*(3^2), so we get n = 36 and we tick the factors for that right!? Now n can be bigger right, the question say for any integer n, so we can have one more 2 in n, making it 72 and that should check 24 and 72 as answers as well. Am I correct or am I missing something? I had come across a similar doubt before as well.
“divisors of every integer n”.
You correctly identified that n = 36k, for some positive integer k. As such, if n = 36 then 72 is clearly not a divisor of n. In fact, for any odd values k may assume, 72 is not a divisor of n.