KöMaL 2009 B4167

For every positive integer $n$, let $f$($n$) denote the number obtained by reversing the order of digits in the decimal form of $n$. (For example, $f$(2500)=52, $f$(1456)=6541.) Find all positive integers $k$, such that for any multiple $n$ of $k$, $k$ also divides the number $f$($n$).