  After defining continuous extensions of binary relations on the set N of
natural numbers to its Stone-Cech compactification \beta N, we establish some
results about one of such extensions. This provides us with one possible
divisibility relation on \beta N and we introduce a few more, defined in a
natural way. For some of them we find equivalent conditions for divisibility.
Finally, we mention a few facts about prime and irreducible elements of (\beta
N, \cdot). The motivation behind all this is to try to translate problems in
number theory into \beta N.
