Is this number divisible by ?
Clarification: The 12 subscript indicates we are working in base 12.
No calculators please! :)
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Note that we are trying to divide by 3 , a number which divides the base we are working in, base 1 2 . Because 3 divides 1 2 , all digits except the first won't affect divisibility (think of dividing by 5 in base 1 0 , or dividing by 2 in base 1 0 ). Thus, we look at the last digit, and it is divisible by 3 , making the number divisible by 3 .