As above, isn't that what the factors give? The factors of base 10 are 2 and 5, adding in the 1 gives you the normal coinage/notage sequence. This is the fewest denominations which gives on average the fewest notes/coins per sum.

If we used hexadecimal money, the factors would be 2, 4 and 8. Adding in the 1 again makes the fewest denominations which gives on average the fewest notes/coins per sum.

Now that I think about it, this would be different for a prime base, of course. So, you're right - it is more complicated. Although any society using a prime base for currency deserves everything they get.