Evaluate
\frac{72157}{8352}\approx 8.639487548
Factor
\frac{59 \cdot 1223}{2 ^ {5} \cdot 3 ^ {2} \cdot 29} = 8\frac{5341}{8352} = 8.63948754789272
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\begin{array}{l}\phantom{8352)}\phantom{1}\\8352\overline{)72157}\\\end{array}
Use the 1^{st} digit 7 from dividend 72157
\begin{array}{l}\phantom{8352)}0\phantom{2}\\8352\overline{)72157}\\\end{array}
Since 7 is less than 8352, use the next digit 2 from dividend 72157 and add 0 to the quotient
\begin{array}{l}\phantom{8352)}0\phantom{3}\\8352\overline{)72157}\\\end{array}
Use the 2^{nd} digit 2 from dividend 72157
\begin{array}{l}\phantom{8352)}00\phantom{4}\\8352\overline{)72157}\\\end{array}
Since 72 is less than 8352, use the next digit 1 from dividend 72157 and add 0 to the quotient
\begin{array}{l}\phantom{8352)}00\phantom{5}\\8352\overline{)72157}\\\end{array}
Use the 3^{rd} digit 1 from dividend 72157
\begin{array}{l}\phantom{8352)}000\phantom{6}\\8352\overline{)72157}\\\end{array}
Since 721 is less than 8352, use the next digit 5 from dividend 72157 and add 0 to the quotient
\begin{array}{l}\phantom{8352)}000\phantom{7}\\8352\overline{)72157}\\\end{array}
Use the 4^{th} digit 5 from dividend 72157
\begin{array}{l}\phantom{8352)}0000\phantom{8}\\8352\overline{)72157}\\\end{array}
Since 7215 is less than 8352, use the next digit 7 from dividend 72157 and add 0 to the quotient
\begin{array}{l}\phantom{8352)}0000\phantom{9}\\8352\overline{)72157}\\\end{array}
Use the 5^{th} digit 7 from dividend 72157
\begin{array}{l}\phantom{8352)}00008\phantom{10}\\8352\overline{)72157}\\\phantom{8352)}\underline{\phantom{}66816\phantom{}}\\\phantom{8352)9}5341\\\end{array}
Find closest multiple of 8352 to 72157. We see that 8 \times 8352 = 66816 is the nearest. Now subtract 66816 from 72157 to get reminder 5341. Add 8 to quotient.
\text{Quotient: }8 \text{Reminder: }5341
Since 5341 is less than 8352, stop the division. The reminder is 5341. The topmost line 00008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.
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}