Question 4.4.10: Dividing in Base 6 Divide 56)34106...
Dividing in Base 6
Divide 5_6)\overline{3410_6}
Step-by-Step
The multiples of 5 in base 6 are
5_6 × 1_6 = 5_6 5_6 × 2_6 = 14_6 5_6 × 3_6 = 23_6
5_6 × 4_6 = 32_6 5_6 × 5_6 = 41_6
\\ \ \ \ 423_6\\ 5_6)\overline{3410_6}\\ \ \ \ \ \ \ 32\\ \ \ \ \ \ \overline{\ \ \ 21\ \ \ }\\ \ \ \ \ \ \ 14 \\ \ \ \ \ \ \overline{ \ \ \ \ \ 30}\\ \ \ \ \ \ \ \ \ \ \ \ 23\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \overline{ \ \ \ 3\ \ }Thus, the quotient is 423_6, with remainder 3_6.
Check: Does (423_6 × 5_6) + 3_6 = 3410_6?
\begin{array}{llll} 423_6 \\× 5_6\\\hline 3403_6\end{array}3403_6 + 3_6 \overset{?}{=} 3410_6
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