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From: rlr@pyuxn.UUCP
Newsgroups: net.math
Subject: Re: Simple Division Properties
Message-ID: <166@pyuxn.UUCP>
Date: Thu, 25-Aug-83 12:13:45 EDT
Article-I.D.: pyuxn.166
Posted: Thu Aug 25 12:13:45 1983
Date-Received: Sat, 27-Aug-83 10:25:54 EDT
References: <548@uw-june>
Organization: Bell Labs, Piscataway
Lines: 17


What hasn't been appropriately noted here is the recursion in the nine rule.

9:  a number is divisible by 9 if the sum of its digits is divisible by 9

OK, so this rule can be applied recursively...

9877898798979877898798976 -->  sum of digits is 198. Is it divisible by 9?
198   (1 + 9 + 8)         -->  sum of digits is 18.  Is it divisible by 9?
18    (1 + 8)             -->  sum of digits is 9.

It always finally resolves to 9.

What about multiplication tricks like how to multiply two digit numbers by 11
(Add the two digits and place the result between them; if > 10 add resulting
ten's digit to hundreds place. 58 * 11 = {5 -- 13 -- 8} = 638).  Any other
multiplication tricks?			Rich