For MMBT2222; How to get hfe value to calcluate minimum base current to drive transistor in Saturation?
The Vce(sat) curves on a typical datasheet for that part don't go under 1mA (see figures 2 and 6). Gain drops at lower current, especially on some older parts, but it's probably >> 20 at 31uA Ic. The MMBT4401, for example, lists minimum hFE as 20 at 100uA, but typically the gain does not drop off as rapidly as that would suggest (see figure 1). 

You are probably safe using Ic/Ib = 10 (as in figure 2), but Ic/Ib = 5 would be even safer, since the datasheet is silent on lower collector currents. 

The minimum is a bad number to use, it will vary from part to part. You want to use a safe number that will saturate any transistor you pull off any given reel of parts and will saturate it at the maximum Ic and over the entire operating temperature range.