Consider base 6. Testing divisibility by 2 and 3 can be done by examining the last digit. Similarly, decimal (hexal hexary) expansions of fractions with those denominators terminate. Testing divisibility for 5 and 7 can be done by methods analogous to 9 and 11 in decimal.

6 = 3! might be useful. Number of faces of a cube.

Previously, base 30.

Inspired by, the fingers on one hand can specify one digit in base 6. Though finger counting is unary.

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