« Nothing More to Say | Main | What's a Pharyngula? »


Vito Prosciutto

Very cool. The 11 test is actually a bit simpler than the version I knew (take the sum of every other digit and subtract the sum of the remaining digits and if that number is divisible by 11 then you're done.

J.D. Fisher

Nice generalization. Very nice work.


Another quick divisibility test for 11:
Any palindromic number (i.e. a number that's written the same forwards or backwards, like 2112 or 12344321) which has an even number of digits is divisible by 11.

The converse isn't true, of course.


thanks for the divisiblity of 7 been tryin to find it =)


hmm, I don't know if you look this far back in your archives. Your divisibility test for 7 is clunky for longer numbers.

Try this instead:

break the number into groups of three digits (breaks go where the commas go). Add the even groups, subtract the odd ones (or vice versa). If the result is divisible by 7, so is the number.

eg: 82,342,509,668

509 + 82 = 591
748 + 668 =1416
1416 - 591 = 825

Now is 825 divisible by 7? Apply your test, which is new to me: 82 - 2(5) = 72. Nope


Oh, and the same test works for 13.

(why? because 1001 = 7*11*13)


If you tests for 11 are true, it would make both 777 AND 767 divisible by 11. Me no thinkee so.


Nici: i don't think your examples disprove my test.

for 777:

77 - 14 = 63, which is divisible by 7.

for 767:

76 - 14 = 62, which isn't.


heyy lol i fink its wierd 2 bcuz i red da comment n its false
767 dont work m8 dus it lol
rite listen, wot it is yeh, is cuz...767 take 7 x2 and yh we so u got 76 - 14 well dat makes 62 n it dont work !!! ur fake m8 i neeed da real answer ne1 got ne help ?

Dumbassatic poker

Umm danielle I hope to god you are joking because you just proved yourself an atard by contradiction... If the answer you get is right you must be wrong? wtf. Oh btw Carlos Mencia just nominated you for DEE DEE DEE of the year congrats!


yepz whateva

Nabi Bux Abro

I want to get the knowledge about the number divisible by 13.


i am a student strugling on a question the question is when 823519 is divided by a number which is bigger than one the remainder is three times the remainder obtained by dividing 274658 by the same number find the divisor?


most easy test


in answer to Nabi Bux Abro's question:

1} 823519 = Ax + 3R
2} 274658 = Cx + R
A, C, R, x are integer unknowns, and 'x' is the divisor that you're looking for.

Subtract 3 times {2} from {1} to get
455 = (A-3C)x +3R - 3R
5*91 = (A-3C)x.
'x' is either 5 or 91. 5 does not work. 91 does, since 823519/91 has remainder 60, and 274658/91 has remainder 20.

Joe Salami

You stupid ham prosciutto, it's the same test, c-(b-a)=c-b+a!


The divisibility test of 7 is good & cool.

toni,bit sindri,barhiya

it is very intelligent work.

emergency response

I ran this divisibility test by myself and get the same results. It's amazing!

Mad Teddy

Check out my web page:


where I present a document which explains how it is possible to generate divisibilty tests for any divisor ending in 1, 3, 7, or 9 (i.e. relatively prime to 10). Starting from the "break off the last digit, double it, and subtract" test for 7, I've presented a table for every number of this type up to 109. It would be a straightforward matter to extend it as far as you like.

(Note that the usual tests for 3, 9, and 11 are actually examples of this type of test, thinly disguised.)

Daniel       Ngila

I must say congrats to whoever figured out the divisibility test of 7.Just for the record i did it when i was 16.No offense.


too hard !!!!!!!

greta gonzales

great!! it helps a lot to math majors students

Silvio Moura Velho

I created a rule for divisibility by seven, eleven and thirteen whose algorithm for divisibility by seven is this:
N = a,bcd; a' ≣ ( − cd mod 7 + a ) mod 7; cd is eliminated and if 7|a'b then 7|N. The procedure is applied from right to left repetitively till the leftmost pair of digits is reached. If the leftmost pair is incomplete consider a = 0.
Example: N = 382,536, using simple language:
36 to 42 = 6; 6 + 2 − 7 = 1 → 15; 15 to 21 = 6; 6 + 3 − 7 = 2 → 28; 7|28 and 7|N.
This rule is mentioned in my unpublished (officially registered) book: "Divisibility by 7, the end of a myth?".
This rule is applied in seconds to large numbers entirely through mental calculation.

The comments to this entry are closed.

The .999... Posts That Made Me Briefly Famous

My Feeble Attempts at Humor

Other blogs I like

  • EvolutionBlog
    He writes mostly about evolution, but he's a math guy.
  • Good Math, Bad Math
    Scienceblogs finally has a math guy!
  • Kung Fu Monkey
    A very smart, high-profile screen writer and comic with sensible politics and an amazing ability to rant
  • Math Spectrometer
    My ideas about life, teaching, and politics
  • Pharyngula
    Biology, lefty politics, and strident anti-Intelligent Design
Blog powered by Typepad