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Muthukumar (Guest)
guest
Apr-01-01, 02:26 PM (EST)
 
"Tests of divisibility"
 
   I came across this question in book called "Mathematical Challenge" by A.Gardiner:

We can say if a number is divisible by 2 by looking at the last digit. Are there other divisibility tests you can find which require only inspection of the last digit of the number ?

I came up with the easy one that if the last digit is 0, the number is divisible by 10.

Are there other such tests? More generally, what is the general method to discover a divisibility test ?

Thanks
Muthukumar (a 30-year old bank clerk working in the Middle East)


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alexb
Charter Member
672 posts
Apr-01-01, 02:34 PM (EST)
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1. "RE: Tests of divisibility"
In response to message #0
 
   >We can say if a number
>is divisible by 2 by
>looking at the last digit.
>Are there other divisibility tests
>you can find which require
>only inspection of the last
>digit of the number ?
>
>
>I came up with the easy
>one that if the last
>digit is 0, the number
>is divisible by 10.
>
>Are there other such tests?

The only another one is divisibility by 5: the last digit must be either 5 or 0.

In general, in base b, inspection of the last digit provides information on divisibility by any factor of b. This is just one among several reasons to prefer base 12 to 10. In base 12, one can immediately tell whether a number is divisible by 2, 3, 4, 6, 12 by only inspecting the last digit.

>More
>generally, what is the general
>method to discover a divisibility
>test ?
>

Either from the Glossary or Arithmetic/Algebra pages follow the links to Divisibility Criteria.

All the best,
Alexander Bogomolny


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Ian
Charter Member
7 posts
Apr-01-01, 07:21 PM (EST)
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2. "RE: Tests of divisibility"
In response to message #1
 
   you can also add all the numbers that make up the number, and if this is a multiple of three, then the number is also.

e.g. 123456789?

1+2+3+4+5+6+7+8+9 = 45
4+5=9

and 9 is a multiple of three, therefore 123456789 is also.
ian


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