Divisible by 3?

Is this number divisible by 3 3 ?

( 122333444455555666666 ) 12 (122333444455555666666)_{12}

Clarification: The 12 subscript indicates we are working in base 12.

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Gimme my calculator! No Yes

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3 solutions

Alex G
Apr 29, 2016

Note that we are trying to divide by 3 3 , a number which divides the base we are working in, base 12 12 . Because 3 3 divides 12 12 , all digits except the first won't affect divisibility (think of dividing by 5 5 in base 10 10 , or dividing by 2 2 in base 10 10 ). Thus, we look at the last digit, and it is divisible by 3 3 , making the number divisible by 3 3 .

Sayak Chatterjee
Apr 29, 2016

Base 12 thus we have to look at last digit. Simply It being 6 the no is divisible by 3. Just don't get afraid of the long no. Build confidence and there you go

Geoff Pilling
Apr 29, 2016

Since we are working in base 12, you only need to look at the last digit, and if it divides by 3 then the number divides by 3. Since the last digit is a 6, y e s \boxed{yes} the number divides by 3.

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