Using long division method Solve 83A6 base 10 ÷ 8 base 16

Divide $8_{16}$ by $8_{16}$.

$$8_{16} \div 8_{16} = 1_{16}$$

Write $1_{16}$ in the quotient. Multiply $1_{16}$ by $8_{16}$ and subtract from $8_{16}$.

$$8_{16} - (1_{16} \times 8_{16}) = 8_{16} - 8_{16} = 0_{16}$$

Bring down the next digit, $3_{16}$.

$$\begin{array}{r} 1\phantom{074_{16}} \\ 8_{16} \overline{) 83A6_{16}} \\ - \underline{8\phantom{3A6_{16}}} \\ 03_{16} \\ \end{array}$$

Divide $03_{16}$ (which is $3_{16}$) by $8_{16}$. Since $3_{16} < 8_{16}$, the result is $0_{16}$.
Write $0_{16}$ in the quotient. Multiply $0_{16}$ by $8_{16}$ and subtract from $3_{16}$.

$$3_{16} - (0_{16} \times 8_{16}) = 3_{16} - 0_{16} = 3_{16}$$

Bring down the next digit, $A_{16}$. This forms $3A_{16}$.

$$\begin{array}{r} 10\phantom{74_{16}} \\ 8_{16} \overline{) 83A6_{16}} \\ - \underline{8\phantom{3A6_{16}}} \\ 03_{16} \\ - \underline{0\phantom{A6_{16}}} \\ 3A_{16} \\ \end{array}$$

Divide $3A_{16}$ by $8_{16}$.
Convert $3A_{16}$ to base 10: $3 \times 16^1 + 10 \times 16^0 = 48 + 10 = 58_{10}$.
The divisor $8_{16}$ is $8_{10}$.

$$58_{10} \div 8_{10} = 7 \text{ with a remainder of } 2$$

So, the next digit in the quotient is $7_{16}$.
Multiply $7_{16}$ by $8_{16}$. In base 10, $7 \times 8 = 56_{10}$.
Convert $56_{10}$ to base 16: $56 \div 16 = 3$ remainder 8. So $56_{10} = 38_{16}$.
Subtract $38_{16}$ from $3A_{16}$.

$$3A_{16} - 38_{16} = 2_{16}$$

Bring down the next digit, $6_{16}$. This forms $26_{16}$.

$$\begin{array}{r} 107\phantom{4_{16}} \\ 8_{16} \overline{) 83A6_{16}} \\ - \underline{8\phantom{3A6_{16}}} \\ 03_{16} \\ - \underline{0\phantom{A6_{16}}} \\ 3A_{16} \\ - \underline{38_{16}} \\ 26_{16} \\ \end{array}$$

Divide $26_{16}$ by $8_{16}$.
Convert $26_{16}$ to base 10: $2 \times 16^1 + 6 \times 16^0 = 32 + 6 = 38_{10}$.
The divisor $8_{16}$ is $8_{10}$.

$$38_{10} \div 8_{10} = 4 \text{ with a remainder of } 6$$

So, the next digit in the quotient is $4_{16}$.
Multiply $4_{16}$ by $8_{16}$. In base 10, $4 \times 8 = 32_{10}$.
Convert $32_{10}$ to base 16: $32 \div 16 = 2$ remainder 0. So $32_{10} = 20_{16}$.
Subtract $20_{16}$ from $26_{16}$.

$$26_{16} - 20_{16} = 6_{16}$$

There are no more digits to bring down. The remainder is $6_{16}$.

$$\begin{array}{r} 1074_{16} \\ 8_{16} \overline{) 83A6_{16}} \\ - \underline{8\phantom{3A6_{16}}} \\ 03_{16} \\ - \underline{0\phantom{A6_{16}}} \\ 3A_{16} \\ - \underline{38_{16}} \\ 26_{16} \\ - \underline{20_{16}} \\ 6_{16} \\ \end{array}$$

The quotient is $1074_{16}$ and the remainder is $6_{16}$.

The final answer is $\text{Quotient: } 1074_{16}, \text{ Remainder: } 6_{16}$.