How many players do you need for M:TG drafting? If you try drafting with too few players, what problems do you get? If you try drafting with too many players, what problems does that cause?
In order to be a sanctioned and rated Magic tournament you need at least 8 players, with no upper limit (though multiples of 8 are generally best). Players are then split into 'pods' based on the number of players attempting to get as close to 8 as possible, while having all pods be roughly equal size. (MTR 7.6 and 10.1) In my experience pods of 6-10 work best.
For just casual drafting you can have as few as 2 players. However the fewer players you have the smaller the pool of cards your pod will have to draft with. This will mean you will have fewer cards for any given archetype so you are more likely to be fighting with your neighbors for the cards you need.
However even though there are fewer cards you will end up seeing a larger proportion of the cards available (for example with a 4 player pod you will see 42/48 [87.5%] cards whereas with 8 players you would see 84/112 [75%]). This would make it so that you have a better idea of what everyone else is playing and make signaling easier.
With pods larger than 8 the problems are almost the opposite of pods smaller than 8. While you are less likely to be fighting with your neighbors for cards since there are more of them, you are also less able to plan ahead. With 8 players in a pod with your first pack you will get 6 of those cards back, an knowing which cards were taken can give you an idea of what other people are playing. If you had more than that you might only be getting 2 cards back, which tells you a lot less because almost all of the cards were gong to be picked anyway.
While a standard draft may not work with a small number of players there are several draft variants that work well (and are even designed for) as few as 2 players.