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Maybe slightly interesting, how many note that only odd tooth counts are used on gears and why?

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Not always odd count for both:

3:23
42 teeth ring
13 teeth pinion

4:57
32 teeth ring
7 teeth pinion

4:86
34 teeth ring
7 teeth pinion

As was explained to me once by an engineer:

The reason for having ratios that are in the decimals is that with each revolution a single tooth on the pinion will not contact the same tooth on the ring with every revolution.

The pinion tooth advances one tooth per revolution so that it will contact each tooth on the ring gear through numerous revolutions.

Hope I explained that correctly.

Frank