Darn, you beat me by a full ten minutes!

851 is also my guess. The second non-trivial solution (i.e., something that's not an integer multiple of 851) would be 5743. However, with that you'd have to assume that the last 12 countries in the list each got exactly 7 shipments, which would be an unlikely coincidence. So 851 it is!

And, I am ashamed to admit, I actually used C++ instead of one of my many wonderful programmable calculators for this exercise. :-(

Viktor