@nikitonsky They *could* have counted many ways — to 9999 on two hands like this image from the 1400s, for example — but this is how they did it.

360: they did maths differently (all fractions, division via multiplication by reciprocal, &c) using pre-computed tables and a “squared circle” approach for trig-ish things (no angles!). 360 was both precise enough for surveying and easy to use with their system.

There’s also an Egyptian astronomy tie-in, but that’s another story…