You can′t divide 21 by 12

or, How base can you get?

Can we find a base in which 21 can be divided by 12 without remainder? And why should we? - Because someone said it couldn't be done. They may well have meant that it can't be done if the base is a positive number - and in fact, if you use base (-5) then 21 = 3 x 12 is true.

Which led me to look at some other results in other bases - not recent discoveries, I might add; the keyboard is ready and willing to work, but occasional bursts of lethargy often hit the typist, in particular Nap Attacks as favoured by Garfield.⁽¹⁾

• 31 = 2 x 13 (base 5)
• 41 = 3 x 14 (base eleven)
• 51 = 3 x 15 (base seven)
• 51 = 4 x 15 (base nineteen)

  In tabular form:

  Number	Bases
  31	5
  41	11
  51	7, 19
  61	29
  71	9, 17, 41
  81	13, 55
  91	11, 31, 71
  T1	23, 89
  E1	13, 19, 29, 49
  and here are some with 2 as unit-figure
  52	8
  72	19
  82	11
  92	34
  T2	19
  E2	14, 53

  and so on ... (to be continued)

  Footnote:
  ⁽¹⁾No, not the President; the cartoon cat.