\5_{6} \overline{) 3410_{6}}\

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Base Division" ], "new_concepts": [], "current_concepts": [ "Base Division", "Base Arithmetic" ] } ## Convert numbers to base 10 $$ \begin{aligned} 5_6 &= 5_{10} \ 3410_6 &= 3 \times 6^3 + 4 \times 6^2 + 1 \times 6^1 + 0 \times 6^0 \ &= 3 \times 216 + 4 \times 36 + 6 + 0 \ &= 648 + 144 + 6 \ &= 798_{10} \end{aligned} $$ ## Perform division in base 10 $$ \begin{aligned} 798 \div 5 &= 159 \text{ R } 3 \end{aligned} $$ ## Convert quotient and remainder back to base 6 $$ \begin{aligned} 159 \div 6 &= 26 \text{ R } 3 \ 26 \div 6 &= 4 \text{ R } 2 \ 4 \div 6 &= 0 \text{ R } 4 \ 159_{10} &= 423_6 \ 3_{10} &= 3_6 \end{aligned} $$ $423_6 \text{ R } 3_6$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Number Theory", "Base Division" ] }

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Explanation:

Convert numbers to base 10

Perform division in base 10

Convert quotient and remainder back to base 6

Answer: