  The paper first covers several properties of the extension of the
divisibility relation to a set ${}^*\hspace{-0.5mm}N$ of nonstandard integers.
After that, a connection is established with the divisibility in the
Stone-\v{C}ech compactification $\beta N$, obtaining an equivalent condition
for divisibility of ultrafilters introduced by the author. Some earlier results
are illuminated by nonstandard methods, and new results on ultrafilters on the
higher levels of the divisibility hierarchy are obtained by means of limits.
