Evaluate
36
Factor
2^{2}\times 3^{2}
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)468}\\\end{array}
Use the 1^{st} digit 4 from dividend 468
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)468}\\\end{array}
Since 4 is less than 13, use the next digit 6 from dividend 468 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)468}\\\end{array}
Use the 2^{nd} digit 6 from dividend 468
\begin{array}{l}\phantom{13)}03\phantom{4}\\13\overline{)468}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}7\\\end{array}
Find closest multiple of 13 to 46. We see that 3 \times 13 = 39 is the nearest. Now subtract 39 from 46 to get reminder 7. Add 3 to quotient.
\begin{array}{l}\phantom{13)}03\phantom{5}\\13\overline{)468}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}78\\\end{array}
Use the 3^{rd} digit 8 from dividend 468
\begin{array}{l}\phantom{13)}036\phantom{6}\\13\overline{)468}\\\phantom{13)}\underline{\phantom{}39\phantom{9}}\\\phantom{13)9}78\\\phantom{13)}\underline{\phantom{9}78\phantom{}}\\\phantom{13)999}0\\\end{array}
Find closest multiple of 13 to 78. We see that 6 \times 13 = 78 is the nearest. Now subtract 78 from 78 to get reminder 0. Add 6 to quotient.
\text{Quotient: }36 \text{Reminder: }0
Since 0 is less than 13, 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}