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

Divisibility in the Stone-\v{C}ech compactification