Quoted from the following article: Gear design - RepRap
"Gears typically have prime (or at least co-prime) numbers of teeth. This is so that the same teeth do not always press against one another, so distributing wear, dirt, oil and squashed fingers etc. evenly across all gear teeth involved.
Bad: 15 and 25 teeth. A bump on the large gear always hits the same 3 teeth on the small gear, creating uneven wear; in this same example a bump of the small gear always hits the same 5 teeth on the large gear. To calculate this first find the Greatest Common Divisor (GCD) of each gear tooth count. e.g. GCD(15,25)=5; then divide this result into the number of teeth in question. E.g. 15/5=3 and 25/5=5.
Good: 16 and 25 teeth. A bump on the large gear (eventually) hits every tooth on the small gear, wearing them all equally.
An even uniform gear wear is achieved by ensuring the tooth counts of the two gears meshing together are “relatively prime” to each other; this occurs when the Greatest Common Divisor (GCD) of each gear tooth count equals 1. e.g. GCD(16,25)=1."