Evaluate
27
Factor
3^{3}
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\begin{array}{l}\phantom{30)}\phantom{1}\\30\overline{)810}\\\end{array}
Use the 1^{st} digit 8 from dividend 810
\begin{array}{l}\phantom{30)}0\phantom{2}\\30\overline{)810}\\\end{array}
Since 8 is less than 30, use the next digit 1 from dividend 810 and add 0 to the quotient
\begin{array}{l}\phantom{30)}0\phantom{3}\\30\overline{)810}\\\end{array}
Use the 2^{nd} digit 1 from dividend 810
\begin{array}{l}\phantom{30)}02\phantom{4}\\30\overline{)810}\\\phantom{30)}\underline{\phantom{}60\phantom{9}}\\\phantom{30)}21\\\end{array}
Find closest multiple of 30 to 81. We see that 2 \times 30 = 60 is the nearest. Now subtract 60 from 81 to get reminder 21. Add 2 to quotient.
\begin{array}{l}\phantom{30)}02\phantom{5}\\30\overline{)810}\\\phantom{30)}\underline{\phantom{}60\phantom{9}}\\\phantom{30)}210\\\end{array}
Use the 3^{rd} digit 0 from dividend 810
\begin{array}{l}\phantom{30)}027\phantom{6}\\30\overline{)810}\\\phantom{30)}\underline{\phantom{}60\phantom{9}}\\\phantom{30)}210\\\phantom{30)}\underline{\phantom{}210\phantom{}}\\\phantom{30)999}0\\\end{array}
Find closest multiple of 30 to 210. We see that 7 \times 30 = 210 is the nearest. Now subtract 210 from 210 to get reminder 0. Add 7 to quotient.
\text{Quotient: }27 \text{Reminder: }0
Since 0 is less than 30, stop the division. The reminder is 0. The topmost line 027 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 27.
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}