Long Division

$$\begin{array}{rll}\text{quotient}& & \\ \text{divisor}\text{enclose}longdiv\text{dividend}& & \\ \underline{\dots }& & \\ \text{remainder}& & \end{array}\to \frac{\text{dividend}}{\text{divisor}}=\text{quotient}+\frac{\text{remainder}}{\text{divisor}}$$

1. Identify the shortest initial sequence of digits $d$ from the dividend (starting from the left) such that $d\ge \text{divisor}$.
2. Compute $q=\lfloor \frac{d}{\text{divisor}}\rfloor$ and write $q$ above the rightmost digit of $d$ (on the quotient line).
3. Write $r=d-\left(\text{divisor}\times q\right)$ below the rightmost digit of $d$.
4. Bring down the next digit of the dividend (if any) to the right of $r$, forming a new number, which becomes the new $d$.
5. Repeat steps 2–4 until all digits of the dividend have been processed.
6. The final $r$ after the last step is the $\text{remainder}$, and the concatenation of all $q$ values forms the $\text{quotient}$.