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Stupid

ivisibility Tricks

101 Ways to Stupefy Your Friends

Appeared in Math

orizons November

2006

Marc Renault Shippensburg University Mathematics Department 1871 Old Main Road Shippensburg, PA 17013 msrenault@ship edu http://webspace ship edu/msrenault/divisibility/

1

Introduction

When is the last time this happened to you? You are stranded on a deserted island without a calculator and for some reason you must determine if 67 is a divisor of 95733553; furthermore, a coconut recently fell on your head and you have completely forgotten how to perform long division.

Of course the above scenario would never happen (we all carry around calculators) but it’s good to know that if we should find ourselves in a similar situation there is an easy divisibility rule for 67: remove the two rightmost digits from the number (in our case, 53), double them (106) and subtract

that from the remaining digits (957335

106 = 957229); the original number

is divisible by 67 if and only if the resulting number is divisible by 67.

If the

resulting

number

is

not

obviously

divisible

by

67

we

can

repeat

the

process

until we get a number that clearly is or is not a multiple of 67. example, we get the following.

In the above

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