Why do the French count so strangely? Today I've heard a talk about division rules. The lecturer stated that base 12 has a lot of division rules and was therefore commonly used in trade.
English and German name their numbers like they count (with 11 and 12 as exception), but not French:
  # |   English |           German | French
-----------------------------------------------
  0 |      zero |            null  | zero
  1 |       one |            eins  | un
  2 |       two |            zwei  | deux
  3 |     three |            drei  | trois
  4 |      four |            vier  | quatre
  5 |      five |            fünf  | cinq
  6 |       six |           sechs  | six
  7 |     seven |          sieben  | sept
  8 |     eight |            acht  | huit
  9 |      nine |            neun  | neuf
 10 |       ten |            zehn  | dix
 11 |    eleven |             elf  | onze
 12 |    twelve |           zwölf  | douze
 13 | thir|teen |       drei|zehn  | treize
 14 | four|teen |       vier|zehn  | quatorze
 15 |  fif|teen |       fünf|zehn  | quinze
 16 |  six|teen |       sech|zehn  | seize
 17 |seven|teen |       sieb|zehn  | dix-sept
            18 and 19 are "regular"
 20 |    twenty |          zwanzig | vingt
 21 |twenty-one |  ein|und|zwanzig | vingt et un
 22 |twenty-two | zwei|und|zwanzig | vingt-deux
            23 - 69 are "regular"
 70 |  seven|ty |         sieb|zig | soixante-dix = 60 + 10
              ....
 80 |   eigh|ty |         acht|zig | quatre-vingts = 4*20 ?!?!
 81 |eighty-one |  ein|und|achtzig | quatre-vingt-un = 4*20 + 1
      ...

So my question is:
Why do French count so strangely after 79?
(Are there other languages that count similar? What's the historic / mathematical reason for this system?)
Related Questions


*

*Why is a full turn of the circle 360°?

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 A: Actually, the French system was designed regularly, i.e. with "septante" for 70, "octante" for 80 and "nonante" for 90. But this system was not accepted at the time (roughly the 16th century), because people were used to the old system ("quatre-vingt", etc.). But the old system remained in Belgium (for "septante" and "nonante") and Switzerland (for "septante, the slightly modified "huitante" in Vaud canton, and "nonante").
A: This is a bit of a guess but I think this has a lot to do with whether the numbering system was rationalised at any point.
If you tell someone from England that you're having trouble sleeping he'll probably suggest you count sheep. I won't attempt a weak joke about having a bedroom full of farm animals. The phrase comes from an old numbering system 
 1  |  yan
 2  |  tan
 3  |  tether  
 4  |  mether
 5  |  pip  
 6  |  nether
 7  |  aether
 8  |  oevro
 9  |  cuevro
10  |  dick
11  |  yanadick
12  |  tanadick
13  |  tetherdick
14  |  methradick
15  |  bumfit
16  |  yanabum
17  |  tanabum
18  |  tetherbum
19  |  metherbum
20  |  jiggit

This died out a long time ago but shepherds kept it up for longer. So to count sheep is to   If you look on Wikipedia there are loads of different ones people counted differently in different areas of the country. (It seems the one my great-granddad taught me isn't in there.)
At some point this was changed by introducing a new numbering system.  Similarly The swedes and Norwegians use a base 10 numbering system today, but they used to use the Danish system. Similarly German (I think) has undergone several standardizations to keep it as one language. It wouldn't surprise me if there used to be less rational German counting systems that died out. 
If the French tried to rationalise their numbering is would have been during the revolution. But as they tried to rationalise everything, including a ten hour day and a decimal calender (Today is Carp the 25th of Flower) A lot of things didn't take off. So I would guess the numbers were one of the things that failed.
A: Many languages have (at least relicts of) non-decimal counting, very often vigesimal (because we have 20 fingers plus toes), but also many other systems. I recommend an old Gutenberg project of mine, The Number Concept
Note for example that the Danish word for 55 is femoghalvtreds "five more than half the third twenty-block"
A: Actually, if you go back in time a bit in English, you'll realise that English was 'strange' too:

Four score and seven years ago our fathers brought forth on this continent a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal.

(The Gettysberg Address, 1863)
Now if you were to translate that into French in 1863, you'd get pretty much what you'd get today:

Il y a quatre-vingt sept ans, nos pères donnèrent naissance sur ce continent à une nouvelle nation conçue dans la liberté et vouée à la thèse selon laquelle tous les hommes sont créés égaux.

Why this has remained the case in French but has changed in English is probably more of a question for French.SE or English.SE.
A: actually numbers from 11 to 16 are quite regular in French (and in Italian) too: they just are a derivation from Latin.
        | French    | Italian       | Latin 
un      | on·ze     | un·dici       | un·decim
deux    | dou·ze    | do·dici       | duo·decim
trois   | trei·ze   | tre·dici      | tre·decim
quatre  | quator·ze | quattor·dici  | quattuor·decim
cinq    | quin·ze   | quin·dici     | quin·decim
six     | sei·ze    | se·dici       | se·decim
sept    | dix-sept  | dici(as)sette | septem·decim
huit    | dix-huit  | dici-otto     | duo·de·viginti
neuf    | dix-neuf  | dici(an)nove  | un·de·viginti

(18 and 19 in Latin are computed as 20-2 and 20-1).
Each language has its own way to cope with small numbers.
A: These numberphile videos explain the irregularity quite well:
Problem with french numbers 
In english 1-12 have individual names and after that we have the -teens (4 and 10, 5 and 10, etc.) similar break point happens at the 17th number in the French number system. The major problem which occurs is at 70s. *The French have no word for 70, they call is 60 and 10 - soixante-dix.*So on, 71 is 60 and 11 till 79. 
Similarly, 80 is also not invented, it is 4 20s, quatre-vingt. 81 is 4 20s 1, quatre-vingt-un. 90 is, 4 20s 10, quatre-vingt-dix. 91 is 4 20s 11, quatre-vignt-onze. 
Finally, they have a word for 100, ceut. 
It looks similar to roman numbers Roman number system, where you repeat the letters to combine the values. X is 10 XX is 20 and so on. 

Another peculiar thing in french grading system, 19 out of 20
A: As former Chinese then French colonists we Vietnamese dropped the Chinese script and took on the Roman alphabets and the Arabic numbers as our own, thank to France. But we didn't take on the French counting system. Ours is very straight forward, and like Chinese, is mostly a monosyllabic language. 
một (one),
hai (two),
ba (three),
Bốn (four),
năm (five),
sáu (six),
bảy (seven),
tám (eight),
chín (nine),
mười (ten),
mười một (ten one = eleven),
mười hai (ten two = twelve),
hai mươi (two tens = 2(10) = 20),
hai mươi một (two tens one = 2(10) + 1 = 21),
ba mươi (three tens = 3(10) = 30),
ba mươi một (three tens one = 3(10) + 1 = 31),
một trăm (one hundred),
một trăm một (one hundred one = 1(100) + 1 = 101),
hai trăm (two hundreds).
A: Ya, right, so strange, so how about to use Chinese count? Maybe a little convenient. :D

  # |   English |           Chinese
----------------------------------------------
  0 |      zero |            零
  1 |       one |            一
  2 |       two |            二
  3 |     three |            三
  4 |      four |            四
  5 |      five |            五
  6 |       six |            六
  7 |     seven |            七
  8 |     eight |            八
  9 |      nine |            九
 10 |       ten |            十
 11 |    eleven |            十|一
 12 |    twelve |            十|二
 13 | thir|teen |            十|三
 14 | four|teen |            十|四
 15 |  fif|teen |            十|五
 16 |  six|teen |            十|六
 17 |seven|teen |            十|七
                             十|八
                             十|九
 20 |    twenty |            二|十
 21 |twenty-one |            二|十|一
 22 |twenty-two |            二|十|二

100,000,000 | 1 hundred million  |  一|亿 （1 followed by eight zeros）
OK, let me show you the 999,999,999.   九亿九千九百九十九万九千九百九十九

Just imagine that what if we use this to do math. ;-P
