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From: jcn@aplvax.UUCP
Newsgroups: net.math
Subject: Re: interesting division by three property
Message-ID: <270@aplvax.UUCP>
Date: Wed, 24-Aug-83 10:23:26 EDT
Article-I.D.: aplvax.270
Posted: Wed Aug 24 10:23:26 1983
Date-Received: Fri, 26-Aug-83 01:37:18 EDT
Organization: JHU/Applied Physics Lab, Laurel, MD
Lines: 44

There are many well known divisibility tests. Here are a few:

A number is divisible by two if the last digit is divisible by 2.

A number is divisible by three if the sum of the digits is divisible by 3.

A number is divisible by four if the last two digits of the number is
divisible by four.

A number is divisible by five if the last digit is 0 or 5.

A number is divisible by six if the sum of the digits is divisible by
three and the number is even (i.e. the number is divisible by both
two and three).

I do not know a divisibility test for seven. I have heard that one exists,
but that it is as difficult to perform as the actual long division.
Anybody know what it is?

A number is divisible by eight if the last three digits of the number are
divisible by eight.

A number is divisible by nine if the sum of the digits is divisible by
nine.

A number is divisible by ten if (surprise! :-)) the last digit is 0.

A number is divisible by eleven if the alternating sum of the digits
is divisible by eleven.

A number is divisible by twelve if the last two digits are divisible by
four and the sum of the digits is divisible by three.


Any others?

A lot of people evidently learned these divisibility rules in elementary
school.  I didn't learn them till I taught them in a freshman math
course.

					John Noble
					JHU/APL
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