Editing Harshad number (section)

== Other bases ==
The harshad numbers in [[duodecimal|base 12]] are:
:1, 2, 3, 4, 5, 6, 7, 8, 9, {{d2}}, {{d3}}, 10, 1{{d2}}, 20, 29, 30, 38, 40, 47, 50, 56, 60, 65, 70, 74, 80, 83, 90, 92, {{d2}}0, {{d2}}1, {{d3}}0, 100, 10{{d2}}, 110, 115, 119, 120, 122, 128, 130, 134, 137, 146, 150, 153, 155, 164, 172, 173, 182, 191, 1{{d2}}0, 1{{d3}}0, 1{{d3}}{{d2}}, 200, ...
where {{d2}} represents ten and {{d3}} represents eleven.

Smallest {{mvar|k}} such that <math>k \cdot n</math> is a base-12 harshad number are (written in base 10):
:1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 6, 4, 3, 10, 2, 11, 3, 4, 1, 7, 1, 12, 6, 4, 3, 11, 2, 11, 3, 1, 5, 9, 1, 12, 11, 4, 3, 11, 2, 11, 1, 4, 4, 11, 1, 16, 6, 4, 3, 11, 2, 1, 3, 11, 11, 11, 1, 12, 11, 5, 7, 9, 1, 7, 3, 3, 9, 11, 1, ...

Smallest {{mvar|k}} such that <math>k \cdot n</math> is not a base-12 harshad number are (written in base 10):
:13, 7, 5, 4, 3, 3, 2, 2, 2, 2, 13, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 157, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 157, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1885, 1, 1, 1, 1, 1, 3, ...

Similar to base 10, not all factorials are harshad numbers in base 12. After 7! (= 5040 = 2{{d3}}00 in base 12, with digit sum 13 in base 12, and 13 does not divide 7!), 1276! is the next that is not. (1276! has digit sum 14201 = 11 × 1291 in base 12, thus does not divide 1276!)