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Comment by cjensen | Hacker News Reader

Base-12 is nice because, like Seximal it is divisible by both the first and second prime number (2 and 3). But it is also divisible by the first prime (2) twice, and doesn't immediately overflow into extra digits.

So 10 in base 12 can be exactly divided by 2, 3, 4, 6, 8, and 9.

Compare this to base 10 where 10 can only be exactly divided by 2, 4, 5, and 8.

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How exactly can 10 be divided by 4 and 8?

In decimal:

10 / 4 = 2.5

2.5 can be represented exactly in decimal. As opposed to:

10 / 3 = 3.33333333333...

which cannot.

In duodecimal (10=dozen, A=ten): 10 / 3 = 4 A / 3 = 3.4

you need an extra blank line, or indent 3 spaces, to preserve linebreaks:

10 / 3 = 4

A / 3 = 3.4

     10 / 3 = 4
     A / 3 = 3.4

Unfortunately, it is too late to edit; but thanks!

Maybe he meant you don't end up with a number with infinite digits?

10/4 = 2.5

vs.

10/3 = 3.33333...

Exact divisors are not what they are cracked up to be. By and large most divisions will wind up falling on an inexact division. One neat property of a prime base is that detecting exact divisions is easy: Just count trailing zeros in your result. E.g:. Ob110010 / 0b101 == 0b1010 which has the expected number of zeros at the end. You can't count on this in decimals, e.g. 50 / 25 == 2.

> Exact divisors are not what they are cracked up to be.

They’re pretty nice if you use base 60, in which case you can figure out how to almost always approximate any division problem by something you already have in your reciprocal table.

Being able to exactly divide by 3 is really helpful. That is why we use 12 for hours, inches, etc.

I would consider a duodecimal (base-12) metric system to be ideal, personally.

Consider: take a log of all divisions done by your computer; how often would those divisions be done by something that is 3 or an exact multiple of 3.

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