I might be mistaken (although I doubt it), but didn't the Maya use a system based in 16? And the Babylonians or one of those cultures use base 12?

Neither one would be hard to achieve. For base 16 just chop off the thumbs and big toes. For base 12, chop off the thumb and index finger and the big toes and the one next to it (index toe?). Want to do binary? Count in base 17? And for base 36 we just take all of those now-unused digits and stick 'em back on.

To all you Luddites who object, I say, "Phooey! You're standing in the Way Of Science!"