Evaluate
36
Factor
2^{2}\times 3^{2}
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\begin{array}{l}\phantom{27)}\phantom{1}\\27\overline{)972}\\\end{array}
Use the 1^{st} digit 9 from dividend 972
\begin{array}{l}\phantom{27)}0\phantom{2}\\27\overline{)972}\\\end{array}
Since 9 is less than 27, use the next digit 7 from dividend 972 and add 0 to the quotient
\begin{array}{l}\phantom{27)}0\phantom{3}\\27\overline{)972}\\\end{array}
Use the 2^{nd} digit 7 from dividend 972
\begin{array}{l}\phantom{27)}03\phantom{4}\\27\overline{)972}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}16\\\end{array}
Find closest multiple of 27 to 97. We see that 3 \times 27 = 81 is the nearest. Now subtract 81 from 97 to get reminder 16. Add 3 to quotient.
\begin{array}{l}\phantom{27)}03\phantom{5}\\27\overline{)972}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}162\\\end{array}
Use the 3^{rd} digit 2 from dividend 972
\begin{array}{l}\phantom{27)}036\phantom{6}\\27\overline{)972}\\\phantom{27)}\underline{\phantom{}81\phantom{9}}\\\phantom{27)}162\\\phantom{27)}\underline{\phantom{}162\phantom{}}\\\phantom{27)999}0\\\end{array}
Find closest multiple of 27 to 162. We see that 6 \times 27 = 162 is the nearest. Now subtract 162 from 162 to get reminder 0. Add 6 to quotient.
\text{Quotient: }36 \text{Reminder: }0
Since 0 is less than 27, stop the division. The reminder is 0. The topmost line 036 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 36.
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}