you don't use a freewheel for a 23 tooth sprocket you need a cassette hub heres gear ratios for ya
Sprocket
F/W or Cassette
22
8
23
8
25
9
28
10
30
11
33
12
36
13
39
14
41
15
44
16
Usually the sprocket is an inseparable part of the freewheel, and the size of the freewheel is determined by the hub.
Unless by freewheel you mean driver (in which case 8-9) I haven't ridden bmx in a few years but last time I checked the smallest freewheel you could buy was 12 tooth which would make for quite a low ratio
I'm assuming you're talking about a BMX here, which use the words a bit different from the rest of the cycling world.So it's the size/tooth count of the freewheel that you're asking about.And then it's just as much about what you want as what you need.When you change the sprocket/freewheel size you change the gear ratio.A big sprocket and a small freewheel lets you go fast, but you'll have to push harder.A bigger freewheel will cost you some top speed, but will make it easier to get the bike moving.A very common combo is 25t front and a 9t rear.
If the driver/freewheel isn't too badly worn you can keep using it even if you replace the sprocket.
a 25 tooth sprocket will fit on a 9 tooth driver
There isn't much need to discuss tooth size as such. The important things are which width of chain the sprocket is intended for and the tooth count. Tooth count decides which gear ratio you get.
It's much more about the hub than it is about the wheel, and fortunately the threading on freewheel hubs is fairly consistent. Simply buy a freewheel that has a 28t sprocket in there and you should be good to go. Freewheels are just about "never" disassembled, but ridden as a unit till they're worn out.
9 tooth driver
13 tooth front/ 40 tooth rear
41 tooth
It uses a 47 tooth sprocket.
45 tooth rear