  This paper describes a new approach to classifying integral factorial ratio,
obtaining in particular a direct proof of a result of Bober. These results
generalize an observation going back to Chebyshev that
$(30n)!n!/((15n)!(10n)!(6n)!)$ is an integer for all $n$. Due to the work of
Rodriguez-Villegas and Beukers and Heckman, this problem is closely related to
classifying hypergeometric functions with finite monodromy groups, and the
result of Bober was originally derived as a consequence of the work of
Beukers--Heckman. The new proof is elementary and makes partial progress on
other related questions.
