Could you help me understand which of the following options are correct? I give my opinion on them, though.

The number 4 is ____ than 5.

The number 4 is
1) lower - correct
2) lesser - correct
3) smaller - correct
4) fewer - wrong
5) less - wrong
than 5.

The number 4 is____than 3.
The number 4 is
6) higher - correct
7) greater - correct
8) bigger - ???
than 3.