Originally Posted by techone
Then if you were saying I was right in that a highest common factor of 1 means a different skidpatch for every tooth on the cog, then it makes sense to me that a 16 tooth cog would have 16 skidpatches and an 18 tooth cog would have 18. So, the 18 would be better for your tires.
(I think this was discussed at length not long ago on the Fixed gear mailing list. Wished I would've paid more attention now, just like in my math classes!...)
Yes, if you're talking about increasing the number of cog teeth while still maintaining relative primeness, then it is better to increase the number of teeth in the drivetrain. But if in increasing the number of teeth, you decrease the relative primeness, then it's a net loss. For example, 48/17 is good (17 patches), 48/18 is less good (3 patches), 48/19 is best of all (19 patches).