the last few are based on the decimal expansion for 1/7 (1/7 = .142857, round up to 143, 2/7 = .285714, round up to 286, etc.) if you always round up you'll get those patterns.
another thing to watch for would be something like 143 x 17 which you could think of as (143 x 10) + (143 x 7) = 1430 + 1001 or 2431.
so 858 x 27 = 8580 + 8580 + 6006 or 23166.
as always, take with a grain of salt. good luck to everyone at regionals!