Originally Posted by jimshapiro
So how do you maximize SPs. It's simple. Use a cog with a lot of teeth and one that yields a remainder of 1 (which always makes gcd = 1). Another way is to use a cog with a prime number of teeth, like 17, in which case gcd always = 1 for any remainder.
Actually a cog with a prime number of teeth doesn't always work, if the chainring is a multiple of the cog (34x17, 51x17, etc). What does work is to choose a chainring and cog such that they are relatively prime, that is that they don't have any common factors (except 1 of course). For example: a 16t cog is not prime, but if you use a 49t chainring, 16 and 49 are relatively prime meaning that that the greatest common factor of the two is 1.
Oh yeah, and it's not remainder, it's GCD.