12, 60, and 360 have more integer divisors than their counterparts 10, 100, and 1000 which makes it much easier to divide things up. This holds for both time and angles (navigation). [Decimal time](https://en.wikipedia.org/wiki/Decimal_time) has been tried but never caught on. Similarly [milliradians](https://en.wikipedia.org/wiki/Milliradian) have been used for angles, but there are several competing standards and for most people and most uses, degrees are just simpler.
12: 1, 2, 3, 4, 6, 12
60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
360: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
vs
10: 1, 2, 5, 10
100: 1, 2, 4, 5, 10, 20, 25, 50, 100
1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000
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