Math Is Fun Forum

ZHero

Real Member

Registered: 2008-06-08

Posts: 1,889

Divisibility test for 7 & 13...

Here's an interesting 'divisibility test' for 7 & 13 i came across; but, sadly, is applicable to numbers with more than 3 digits only!

Divide the number into groups of 3 (starting from Right) and find the difference between the sum of the numbers in odd and even places.. If the difference is '0' or a multiple of 7 or 13 (as the case may be), its divisible by it!

e.g. 4537764
==> 4  537  764
==> (764+4) - (537)
==> 231= 7*33 ! Hence divisible!

Last edited by ZHero (2008-07-19 10:02:18)

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If two or more thoughts intersect, there has to be a point!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Divisibility test for 7 & 13...

Thanks ZHero ... why does it work?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Divisibility test for 7 & 13...

We do ... just have limited memory capacity

(Please don't yell)

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Divisibility test for 7 & 13...

you are really angry today jane...what's wrong?
yelling in several posts

Who is jane?

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

Re: Divisibility test for 7 & 13...

you are really angry today jane...what's wrong?
yelling in several posts

Who is jane?

JaneFairfax is a member with close to 7000 posts! I personally feel the member in question is smart!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: Divisibility test for 7 & 13...

you are really angry today jane...what's wrong?
yelling in several posts

Who is jane?

JaneFairfax is a member with close to 7000 posts! I personally feel the member in question is smart!

Oh, a deleted post, then?

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

Re: Divisibility test for 7 & 13...

Who is jane?

JaneFairfax is a member with close to 7000 posts! I personally feel the member in question is smart!

Oh, a deleted post, then?

The individual continues to be a member.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: Divisibility test for 7 & 13...

If the number (y) is odd and divisible by 7........

(y -1)/2=a
If a is odd, b = (a-1) / 2, if a is even b = (a +y-1) / 2
If b is odd, c = (b-1) / 2, if b is even c = (a +y-1) / 2
If y is divisible by 7, c will be divisible by 7..........

Works for any Mersenne Number....

Works because whatever I do to y to get to zero I have to be able to do to a multiple of y, to get to a remainder zero for y! And 7-1/2=3 3-1/2=1 1-1/2=0.

Example:35= 5*7,
35-1/2=17, 17-1/2=8 (8+35-1)/2=21,
21= 3*7

Example: 27=3*9
27-1/2=13 13-1/2=6
6=3*2

3-1/2=1
1-1/2=0

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"Time not important. Only life important." - The Fifth Element 1997