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\begin{array}{l}\phantom{314)}\phantom{1}\\314\overline{)314}\\\end{array}
Use the 1^{st} digit 3 from dividend 314
\begin{array}{l}\phantom{314)}0\phantom{2}\\314\overline{)314}\\\end{array}
Since 3 is less than 314, use the next digit 1 from dividend 314 and add 0 to the quotient
\begin{array}{l}\phantom{314)}0\phantom{3}\\314\overline{)314}\\\end{array}
Use the 2^{nd} digit 1 from dividend 314
\begin{array}{l}\phantom{314)}00\phantom{4}\\314\overline{)314}\\\end{array}
Since 31 is less than 314, use the next digit 4 from dividend 314 and add 0 to the quotient
\begin{array}{l}\phantom{314)}00\phantom{5}\\314\overline{)314}\\\end{array}
Use the 3^{rd} digit 4 from dividend 314
\begin{array}{l}\phantom{314)}001\phantom{6}\\314\overline{)314}\\\phantom{314)}\underline{\phantom{}314\phantom{}}\\\phantom{314)999}0\\\end{array}
Find closest multiple of 314 to 314. We see that 1 \times 314 = 314 is the nearest. Now subtract 314 from 314 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }0
Since 0 is less than 314, stop the division. The reminder is 0. The topmost line 001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}