AUSTRIAN-POLISH 1984 Problem 2

Let $A$ be the set of four-digit natural numbers having exactly two distinct digits, none of which is zero. Interchanging the two digits of $n\in A$ yields a number $f (n) \in A$ (for instance, $f (3111) = 1333$ ). Find those $n \in A$ with $n > f (n)$ for which $gcd(n, f (n))$ is the largest possible.