reading these answers i think there is some misunderstanding re: what is meant by integer ratios. For most gear sets (whether spur, helical, etc) the ratio is the ratio of the number of teeth which is obviously an integer ratio.
Example a typical example differential might have a 41 tooth ring and 11 tooth pinion for a ratio of
41:11. That is typically expressed in decimal which is
3.72727272...:1 which is typically rounded off to
3.73:1. The actual ratio remains a ratio of integers.
if you have a transmission with a sequence of gears you would multiply all the integer ratios and still have an overall integer ratio.
A bit aside to the question, in this example common teeth repeat contact only every 11 revs of the big gear, and every tooth combination meshes an equal number of times. The reason cited by @ahipsterpeterpan may be why Chevy chose prime numbers for the tooth count.