Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{180)}\phantom{1}\\180\overline{)2160}\\\end{array}
Use the 1^{st} digit 2 from dividend 2160
\begin{array}{l}\phantom{180)}0\phantom{2}\\180\overline{)2160}\\\end{array}
Since 2 is less than 180, use the next digit 1 from dividend 2160 and add 0 to the quotient
\begin{array}{l}\phantom{180)}0\phantom{3}\\180\overline{)2160}\\\end{array}
Use the 2^{nd} digit 1 from dividend 2160
\begin{array}{l}\phantom{180)}00\phantom{4}\\180\overline{)2160}\\\end{array}
Since 21 is less than 180, use the next digit 6 from dividend 2160 and add 0 to the quotient
\begin{array}{l}\phantom{180)}00\phantom{5}\\180\overline{)2160}\\\end{array}
Use the 3^{rd} digit 6 from dividend 2160
\begin{array}{l}\phantom{180)}001\phantom{6}\\180\overline{)2160}\\\phantom{180)}\underline{\phantom{}180\phantom{9}}\\\phantom{180)9}36\\\end{array}
Find closest multiple of 180 to 216. We see that 1 \times 180 = 180 is the nearest. Now subtract 180 from 216 to get reminder 36. Add 1 to quotient.
\begin{array}{l}\phantom{180)}001\phantom{7}\\180\overline{)2160}\\\phantom{180)}\underline{\phantom{}180\phantom{9}}\\\phantom{180)9}360\\\end{array}
Use the 4^{th} digit 0 from dividend 2160
\begin{array}{l}\phantom{180)}0012\phantom{8}\\180\overline{)2160}\\\phantom{180)}\underline{\phantom{}180\phantom{9}}\\\phantom{180)9}360\\\phantom{180)}\underline{\phantom{9}360\phantom{}}\\\phantom{180)9999}0\\\end{array}
Find closest multiple of 180 to 360. We see that 2 \times 180 = 360 is the nearest. Now subtract 360 from 360 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 180, stop the division. The reminder is 0. The topmost line 0012 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 12.
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}