Associated Topics || Dr. Math Home || Search Dr. Math

### 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
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/

```
Associated Topics:
Elementary Division

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search