For questions like this, it's best to just start listing the numbers that are "tri-factorable" (by listing numbers that are made by multiplying 3 consecutive positive integers, starting with the lowest positive integers we can). It won't take us long:
1 x 2 x 3 =
6
2 x 3 x 4 =
24
3 x 4 x 5 =
60
4 x 5 x 6 =
120
5 x 6 x 7 =
210
6 x 7 x 8 =
336
7 x 8 x 9 =
504
8 x 9 x 10 =
720
9 x 10 x 11 =
990
10x11x12 = 1320 (Oops, too high!)
So how many were under 1000?
9 of them.
