Re: tell me if this is right.

From: Michael Stemper (mstemper_at_siemens-emis.com)
Date: 07/15/04 

Date: Thu, 15 Jul 2004 12:42:50 -0500

In article <cd655f$dpk@odbk17.prod.google.com>, slag writes:
>LarryLard wrote:

>> Here it's easy
>> to see that numerator and denominator share a common factor of 2
>> (since they are both even), so we can immediately say
>>
>> 13142/15048 = 6571/7524
>
>Yeah i've forgotten those tricks. Any number ending in an even number
>or zero

No need to say "an even number or zero". Just say "an even number".
Zero *is* even.

>> Obviously,
>> common factors of 2 and 5 are the easiest to see by inspection; there
>> are 'quick' methods for spotting divisibility by 3, 9, and 11 as well
>> (and others maybe)
>
>What are the tricks for 3, 9, 11 ?

Sum of the digits for 3 and 9. Eleven's a little more subtle. [1]

"Sum of the digits?" he asked.

Add up all of the digits in a number. If the sum is divisible by three,
the number itself is divisible by three. If the sum is divisible by
nine, the number itself is. For instance, take 48: 4+8 is 12, which is
divisible by three, so 48 must be as well. Or, if you like, you can
apply the rule repeatedly: 4+8 is 12. 1+2 is 3, which is divisible by
three.

This rule shows us something interesting. If you have a number that is
a multiple of three, you can stick any number of 0s, 3s, 6s, and 9s
anywhere you want -- beginning, middle or end -- and get another
multiple of three.

For instance, now that we've established that 48 is a multiple of
three, we immediately know that 963049630899336600 is a multiple
of three. (We might not care, but that doesn't change the facts!
Wierd, huh?)

Or, we can also put in *pairs* of digits that add up to a multiple
of three. Given that 48's good, we can go 48484848 or 4444488888.
Or, we can even mix up the two rules: 4033302727270999908!

The same thing holds true for multiples of nine, except that you
have to s/three/nine/g .

[1] Hopefully, nobody's read down this far, or it'll become obvious
that I don't actually *remember* the rule for eleven. Add the even
digits, subtract the odd, something like that. 

-- 
Michael F. Stemper
#include <Standard_Disclaimer>
Build a man a fire, and you warm him for a day. Set him on fire, 
and you warm him for a lifetime.

Relevant Pages

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