Date: Thu, 01 Nov 2007 12:36:37 -0300
David Cressey wrote:
> "Bob Badour" <bbadour_at_pei.sympatico.ca> wrote in message
>>It's ironic you should mention base 9. It's a little-known fact that, if >>a number is evenly divisible by 8, the sum of the digits of the number >>in base 9 is also evenly divisible by 8. And if one repeats the process >>with that sum until the resulting sum has only one digit and if the >>original number was divisible by 8, the one remaining digit will be 8. >> >>It's like magic. So it's really ironic you should mention base 9 in >>particular.
> This is a joke, right? For radix n, n-1 has this interesting property.
> Likewise, 9 has this fun property in decimals. Bookkeepers in the Bob
> Chratchit era used a property much like this one for error detection in
> manually managed numbers.
> If this were another person posting, I'd think it was simple oversight.
> But you, BB, are likely to know exactly what I've just said.
If the number is divisible by any factor of n-1, the sum of the digits
will be a multiple of that factor too. Thus, if one repeatedly sums the
digits of a hexadecimal number, one can tell very quickly whether the
number is divisible by 3, 5 or F.
Base 9 is actually a little less useful because it can only tell you if
the number is divisible by 2, 4 or 8, and these are often relatively
obvious in other bases in any case.
Base 9 is actually a little less useful because it can only tell you if the number is divisible by 2, 4 or 8, and these are often relatively obvious in other bases in any case.Received on Thu Nov 01 2007 - 16:36:37 CET