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Re: Divisibility rule for 7
Posted:
Jul 14, 2006 7:16 PM
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Rajnish Kumar wrote:
> does anyone know the divisibility rule for 7?
It is easy to come up with a rule using congruence consdierations,
namely that 1 is congurent to 1, 10 is congruent to 3, and 1000 is
congruent to 2 mod 7 (if you don't know what this means, never mind).
However in practice, when I want to astound your friends by determining
whether or not a given number is divisible by 7, I use the following
procedure based on the fact that adding or subtracting multiples of 7
and dividing by 10 do not change the divisibility of a number by 7:
1)Take the number and add or subtract a convenient multiple of 7 so
that it now ends in 0.
2) Remove the 0.
3) Repeat the above 2 steps until you reach a number that is small
enough that you can tell without any help that it is divisible by 7.
Example: 243543
1) Add 7 to get 243550
2) Remove the 0 to get 24355
3) Subtract 35 to get 24320
4) Remove the 0 to get 2432
5) Add 26 to get 2460
6) Remove the 0 to get 246
7) Add 14 to get 260
8) Remove the 0 to get 26
9) Observe that 26 is not divisible by 7, and therefore 243543 is also
not divisible by 7.
Although this may seem like a lot of steps, they are easy to perform
accurately in your head.
Note that this algorithm works for determining divisibility by anything
not divisible by either 2 or 5, but there are easier tests for 3, 9,
and 11 that are very well known.
I do not claim originality for this method. They were shown to me by
Douglas Burke when he was in high school and factored numbers in his
head as a nervous habit.
Regards,
Achava
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