Can't divide 16 by 3 though; the nice thing about 12 is that you get nice natural numbers for many common divisors:

  >>> 12/2, 12/3, 12/4, 12/5, 12/6, 12/7, 12/8
  (6.0, 4.0, 3.0, 2.4, 2.0, 1.7142857142857142, 1.5)

  >>> 16/2, 16/3, 16/4, 16/5, 16/6, 16/7, 16/8
  (8.0, 5.333333333333333, 4.0, 3.2, 2.6666666666666665, 2.2857142857142856, 2.0)

With base-12, only 7 is awkward (and that's probably okay as it's not that common) and the non-natural numbers of 2.4 and 1.5 when dividing by 5 and 8 are still fairly easy to deal with. Dividing by the common figures of 2, 3, and 4 gives nice numbers.

Base-16 has the "infinite number problem" for 3 and 6 that base-10 has, and only 2, 4, and 8 give natural numbers.

This is probably why there are 12 months and why people used "a dozen" for a long time.