A change in a natural number $n$ consists of adding a pair of zeros between two digits or at the end of the decimal representation of $n$. A countryman of $n$ is a number that can be obtained from one or more changes in $n$. For example. $40041$, $4410000$ and $4004001$ are all countrymen from $441$. Determine all the natural numbers $n$ for which there is a natural number m with the property that $n$ divides $m$ and all the countrymen of $m$.