Let us assume you have a base resistor of 1K.
When the transistor is on it will have 0.6V across the emitter / base. So if the emitter sits as high as it can it is at 4.4V.
Base current will then be 0.6 / 1000 = 0.6 mV
If you have a collector current of 140mA you need a current gain of at least
140 / 0.6 = 233 times
Do the same calculation for other values of base resistor.