Rule for dividing by 7

Date: Thu, 1 Dec 1994 08:17:25 -0600 (CST)
From: Daniel Sanfilippo
Subject: Divisibility rules

Many years ago, I taught from a math text that gave "divisibility 
rules" for the numbers one through ten. For example, "if the sum 
of the digits of a number is divisible by three, the number is 
divisible by three."

I remember the rules for all the numbers except "7". I do remember 
that this rule was rather complicated and cumbersome, but it was 
still useful. I've looked in every reference book I could think 
of, but have had no luck.

Any chance you could help me out here?  It would certainly be 
appreciated.

Dan Sanfilippo
Sixth Grade Teacher
Masters Elementary School
Omaha, NE

Date: Thu, 01 Dec 1994 18:56:12 -0500
From: Daniel Eisenbud
Organization: Geometry Forum
Subject: Re: Divisibility rules

I do remember the rule. To find out if a number is divisible by 
seven, you take the last digit, double it, and subtract it from 
the rest of the number.  So if you had 203, you would double the 
last digit to get six, and subtract that to get 14.  If you get an 
answer divisible by 7 (including zero, of course) then the 
original number is divisible by seven; if you don't know the new 
number's divisibility, you can apply the rule again.

A summary of divisibility rules from 3 to 13, with explanations 
for why they work, can be found at

  http://mathforum.org/k12/mathtips/division.tips.html   

-Doctor Dan Eisenbud,  The Geometry Forum
 Check out our web site!  http://mathforum.org/dr.math/