Evaluate
12
Factor
2^{2}\times 3
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\begin{array}{l}\phantom{333)}\phantom{1}\\333\overline{)3996}\\\end{array}
Use the 1^{st} digit 3 from dividend 3996
\begin{array}{l}\phantom{333)}0\phantom{2}\\333\overline{)3996}\\\end{array}
Since 3 is less than 333, use the next digit 9 from dividend 3996 and add 0 to the quotient
\begin{array}{l}\phantom{333)}0\phantom{3}\\333\overline{)3996}\\\end{array}
Use the 2^{nd} digit 9 from dividend 3996
\begin{array}{l}\phantom{333)}00\phantom{4}\\333\overline{)3996}\\\end{array}
Since 39 is less than 333, use the next digit 9 from dividend 3996 and add 0 to the quotient
\begin{array}{l}\phantom{333)}00\phantom{5}\\333\overline{)3996}\\\end{array}
Use the 3^{rd} digit 9 from dividend 3996
\begin{array}{l}\phantom{333)}001\phantom{6}\\333\overline{)3996}\\\phantom{333)}\underline{\phantom{}333\phantom{9}}\\\phantom{333)9}66\\\end{array}
Find closest multiple of 333 to 399. We see that 1 \times 333 = 333 is the nearest. Now subtract 333 from 399 to get reminder 66. Add 1 to quotient.
\begin{array}{l}\phantom{333)}001\phantom{7}\\333\overline{)3996}\\\phantom{333)}\underline{\phantom{}333\phantom{9}}\\\phantom{333)9}666\\\end{array}
Use the 4^{th} digit 6 from dividend 3996
\begin{array}{l}\phantom{333)}0012\phantom{8}\\333\overline{)3996}\\\phantom{333)}\underline{\phantom{}333\phantom{9}}\\\phantom{333)9}666\\\phantom{333)}\underline{\phantom{9}666\phantom{}}\\\phantom{333)9999}0\\\end{array}
Find closest multiple of 333 to 666. We see that 2 \times 333 = 666 is the nearest. Now subtract 666 from 666 to get reminder 0. Add 2 to quotient.
\text{Quotient: }12 \text{Reminder: }0
Since 0 is less than 333, 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}