Evaluate
\frac{612}{37}\approx 16.540540541
Factor
\frac{2 ^ {2} \cdot 3 ^ {2} \cdot 17}{37} = 16\frac{20}{37} = 16.54054054054054
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\begin{array}{l}\phantom{1036)}\phantom{1}\\1036\overline{)17136}\\\end{array}
Use the 1^{st} digit 1 from dividend 17136
\begin{array}{l}\phantom{1036)}0\phantom{2}\\1036\overline{)17136}\\\end{array}
Since 1 is less than 1036, use the next digit 7 from dividend 17136 and add 0 to the quotient
\begin{array}{l}\phantom{1036)}0\phantom{3}\\1036\overline{)17136}\\\end{array}
Use the 2^{nd} digit 7 from dividend 17136
\begin{array}{l}\phantom{1036)}00\phantom{4}\\1036\overline{)17136}\\\end{array}
Since 17 is less than 1036, use the next digit 1 from dividend 17136 and add 0 to the quotient
\begin{array}{l}\phantom{1036)}00\phantom{5}\\1036\overline{)17136}\\\end{array}
Use the 3^{rd} digit 1 from dividend 17136
\begin{array}{l}\phantom{1036)}000\phantom{6}\\1036\overline{)17136}\\\end{array}
Since 171 is less than 1036, use the next digit 3 from dividend 17136 and add 0 to the quotient
\begin{array}{l}\phantom{1036)}000\phantom{7}\\1036\overline{)17136}\\\end{array}
Use the 4^{th} digit 3 from dividend 17136
\begin{array}{l}\phantom{1036)}0001\phantom{8}\\1036\overline{)17136}\\\phantom{1036)}\underline{\phantom{}1036\phantom{9}}\\\phantom{1036)9}677\\\end{array}
Find closest multiple of 1036 to 1713. We see that 1 \times 1036 = 1036 is the nearest. Now subtract 1036 from 1713 to get reminder 677. Add 1 to quotient.
\begin{array}{l}\phantom{1036)}0001\phantom{9}\\1036\overline{)17136}\\\phantom{1036)}\underline{\phantom{}1036\phantom{9}}\\\phantom{1036)9}6776\\\end{array}
Use the 5^{th} digit 6 from dividend 17136
\begin{array}{l}\phantom{1036)}00016\phantom{10}\\1036\overline{)17136}\\\phantom{1036)}\underline{\phantom{}1036\phantom{9}}\\\phantom{1036)9}6776\\\phantom{1036)}\underline{\phantom{9}6216\phantom{}}\\\phantom{1036)99}560\\\end{array}
Find closest multiple of 1036 to 6776. We see that 6 \times 1036 = 6216 is the nearest. Now subtract 6216 from 6776 to get reminder 560. Add 6 to quotient.
\text{Quotient: }16 \text{Reminder: }560
Since 560 is less than 1036, stop the division. The reminder is 560. The topmost line 00016 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 16.
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}