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> If the $81$ digit number $111\cdots 1$ is divided by $729$, the remainder is?
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$729=9^3$

For any number to be divisible by $9$, the sum of the digits have to be divisible by $9$. The given number is divisible by $9$.

Then I tried dividing the given number by $9$. The quotient was like $123456789012\cdots$

So the quotients sum is $(45\times 8)+1=361$

Is this the way to proceed? Is there a shorter way?