Evaluate
\frac{2074464}{6313}\approx 328.60193252
Factor
\frac{2 ^ {5} \cdot 3 ^ {3} \cdot 7 ^ {4}}{59 \cdot 107} = 328\frac{3800}{6313} = 328.60193252019644
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\begin{array}{l}\phantom{25252)}\phantom{1}\\25252\overline{)8297856}\\\end{array}
Use the 1^{st} digit 8 from dividend 8297856
\begin{array}{l}\phantom{25252)}0\phantom{2}\\25252\overline{)8297856}\\\end{array}
Since 8 is less than 25252, use the next digit 2 from dividend 8297856 and add 0 to the quotient
\begin{array}{l}\phantom{25252)}0\phantom{3}\\25252\overline{)8297856}\\\end{array}
Use the 2^{nd} digit 2 from dividend 8297856
\begin{array}{l}\phantom{25252)}00\phantom{4}\\25252\overline{)8297856}\\\end{array}
Since 82 is less than 25252, use the next digit 9 from dividend 8297856 and add 0 to the quotient
\begin{array}{l}\phantom{25252)}00\phantom{5}\\25252\overline{)8297856}\\\end{array}
Use the 3^{rd} digit 9 from dividend 8297856
\begin{array}{l}\phantom{25252)}000\phantom{6}\\25252\overline{)8297856}\\\end{array}
Since 829 is less than 25252, use the next digit 7 from dividend 8297856 and add 0 to the quotient
\begin{array}{l}\phantom{25252)}000\phantom{7}\\25252\overline{)8297856}\\\end{array}
Use the 4^{th} digit 7 from dividend 8297856
\begin{array}{l}\phantom{25252)}0000\phantom{8}\\25252\overline{)8297856}\\\end{array}
Since 8297 is less than 25252, use the next digit 8 from dividend 8297856 and add 0 to the quotient
\begin{array}{l}\phantom{25252)}0000\phantom{9}\\25252\overline{)8297856}\\\end{array}
Use the 5^{th} digit 8 from dividend 8297856
\begin{array}{l}\phantom{25252)}00003\phantom{10}\\25252\overline{)8297856}\\\phantom{25252)}\underline{\phantom{}75756\phantom{99}}\\\phantom{25252)9}7222\\\end{array}
Find closest multiple of 25252 to 82978. We see that 3 \times 25252 = 75756 is the nearest. Now subtract 75756 from 82978 to get reminder 7222. Add 3 to quotient.
\begin{array}{l}\phantom{25252)}00003\phantom{11}\\25252\overline{)8297856}\\\phantom{25252)}\underline{\phantom{}75756\phantom{99}}\\\phantom{25252)9}72225\\\end{array}
Use the 6^{th} digit 5 from dividend 8297856
\begin{array}{l}\phantom{25252)}000032\phantom{12}\\25252\overline{)8297856}\\\phantom{25252)}\underline{\phantom{}75756\phantom{99}}\\\phantom{25252)9}72225\\\phantom{25252)}\underline{\phantom{9}50504\phantom{9}}\\\phantom{25252)9}21721\\\end{array}
Find closest multiple of 25252 to 72225. We see that 2 \times 25252 = 50504 is the nearest. Now subtract 50504 from 72225 to get reminder 21721. Add 2 to quotient.
\begin{array}{l}\phantom{25252)}000032\phantom{13}\\25252\overline{)8297856}\\\phantom{25252)}\underline{\phantom{}75756\phantom{99}}\\\phantom{25252)9}72225\\\phantom{25252)}\underline{\phantom{9}50504\phantom{9}}\\\phantom{25252)9}217216\\\end{array}
Use the 7^{th} digit 6 from dividend 8297856
\begin{array}{l}\phantom{25252)}0000328\phantom{14}\\25252\overline{)8297856}\\\phantom{25252)}\underline{\phantom{}75756\phantom{99}}\\\phantom{25252)9}72225\\\phantom{25252)}\underline{\phantom{9}50504\phantom{9}}\\\phantom{25252)9}217216\\\phantom{25252)}\underline{\phantom{9}202016\phantom{}}\\\phantom{25252)99}15200\\\end{array}
Find closest multiple of 25252 to 217216. We see that 8 \times 25252 = 202016 is the nearest. Now subtract 202016 from 217216 to get reminder 15200. Add 8 to quotient.
\text{Quotient: }328 \text{Reminder: }15200
Since 15200 is less than 25252, stop the division. The reminder is 15200. The topmost line 0000328 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 328.
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}