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\begin{array}{l}\phantom{585)}\phantom{1}\\585\overline{)585}\\\end{array}
Use the 1^{st} digit 5 from dividend 585
\begin{array}{l}\phantom{585)}0\phantom{2}\\585\overline{)585}\\\end{array}
Since 5 is less than 585, use the next digit 8 from dividend 585 and add 0 to the quotient
\begin{array}{l}\phantom{585)}0\phantom{3}\\585\overline{)585}\\\end{array}
Use the 2^{nd} digit 8 from dividend 585
\begin{array}{l}\phantom{585)}00\phantom{4}\\585\overline{)585}\\\end{array}
Since 58 is less than 585, use the next digit 5 from dividend 585 and add 0 to the quotient
\begin{array}{l}\phantom{585)}00\phantom{5}\\585\overline{)585}\\\end{array}
Use the 3^{rd} digit 5 from dividend 585
\begin{array}{l}\phantom{585)}001\phantom{6}\\585\overline{)585}\\\phantom{585)}\underline{\phantom{}585\phantom{}}\\\phantom{585)999}0\\\end{array}
Find closest multiple of 585 to 585. We see that 1 \times 585 = 585 is the nearest. Now subtract 585 from 585 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }0
Since 0 is less than 585, 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}