solution: We may carry out long division in base 5 just as in base 10. We have  \[
  \begin{array}{c|ccc}
  \multicolumn{2}{r}{2} & 0 & 4 \\
  \cline{2-4}
  2 & 4 & 1 & 3 \\
  \multicolumn{2}{r}{4} & \downarrow & \\ \cline{2-2}
  \multicolumn{2}{r}{0} & 1 & \\
  \multicolumn{2}{r}{} & 0 & \downarrow \\ \cline{3-3}
  \multicolumn{2}{r}{} & 1 & 3 \\
  \multicolumn{2}{r}{} & 1 & 3 \\ \cline{3-4}
  \multicolumn{2}{r}{} & & 0
  \end{array}
  \]for a quotient of $\boxed{204_5}$. Note that in the above calculation we have used that $13_5$ divided by $2_5$ is $4_5$, which follows from $4_5\times2_5=8_{10}=13_5$.
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Express the quotient $413_5 \div 2_5$ in base 5.
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: 204_5
extra_info.question: Express the quotient $413_5 \div 2_5$ in base 5.
extra_info.split: test