Evaluate
\frac{20605}{96}\approx 214.635416667
Factor
\frac{5 \cdot 13 \cdot 317}{2 ^ {5} \cdot 3} = 214\frac{61}{96} = 214.63541666666666
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\begin{array}{l}\phantom{240000)}\phantom{1}\\240000\overline{)51512500}\\\end{array}
Use the 1^{st} digit 5 from dividend 51512500
\begin{array}{l}\phantom{240000)}0\phantom{2}\\240000\overline{)51512500}\\\end{array}
Since 5 is less than 240000, use the next digit 1 from dividend 51512500 and add 0 to the quotient
\begin{array}{l}\phantom{240000)}0\phantom{3}\\240000\overline{)51512500}\\\end{array}
Use the 2^{nd} digit 1 from dividend 51512500
\begin{array}{l}\phantom{240000)}00\phantom{4}\\240000\overline{)51512500}\\\end{array}
Since 51 is less than 240000, use the next digit 5 from dividend 51512500 and add 0 to the quotient
\begin{array}{l}\phantom{240000)}00\phantom{5}\\240000\overline{)51512500}\\\end{array}
Use the 3^{rd} digit 5 from dividend 51512500
\begin{array}{l}\phantom{240000)}000\phantom{6}\\240000\overline{)51512500}\\\end{array}
Since 515 is less than 240000, use the next digit 1 from dividend 51512500 and add 0 to the quotient
\begin{array}{l}\phantom{240000)}000\phantom{7}\\240000\overline{)51512500}\\\end{array}
Use the 4^{th} digit 1 from dividend 51512500
\begin{array}{l}\phantom{240000)}0000\phantom{8}\\240000\overline{)51512500}\\\end{array}
Since 5151 is less than 240000, use the next digit 2 from dividend 51512500 and add 0 to the quotient
\begin{array}{l}\phantom{240000)}0000\phantom{9}\\240000\overline{)51512500}\\\end{array}
Use the 5^{th} digit 2 from dividend 51512500
\begin{array}{l}\phantom{240000)}00000\phantom{10}\\240000\overline{)51512500}\\\end{array}
Since 51512 is less than 240000, use the next digit 5 from dividend 51512500 and add 0 to the quotient
\begin{array}{l}\phantom{240000)}00000\phantom{11}\\240000\overline{)51512500}\\\end{array}
Use the 6^{th} digit 5 from dividend 51512500
\begin{array}{l}\phantom{240000)}000002\phantom{12}\\240000\overline{)51512500}\\\phantom{240000)}\underline{\phantom{}480000\phantom{99}}\\\phantom{240000)9}35125\\\end{array}
Find closest multiple of 240000 to 515125. We see that 2 \times 240000 = 480000 is the nearest. Now subtract 480000 from 515125 to get reminder 35125. Add 2 to quotient.
\begin{array}{l}\phantom{240000)}000002\phantom{13}\\240000\overline{)51512500}\\\phantom{240000)}\underline{\phantom{}480000\phantom{99}}\\\phantom{240000)9}351250\\\end{array}
Use the 7^{th} digit 0 from dividend 51512500
\begin{array}{l}\phantom{240000)}0000021\phantom{14}\\240000\overline{)51512500}\\\phantom{240000)}\underline{\phantom{}480000\phantom{99}}\\\phantom{240000)9}351250\\\phantom{240000)}\underline{\phantom{9}240000\phantom{9}}\\\phantom{240000)9}111250\\\end{array}
Find closest multiple of 240000 to 351250. We see that 1 \times 240000 = 240000 is the nearest. Now subtract 240000 from 351250 to get reminder 111250. Add 1 to quotient.
\begin{array}{l}\phantom{240000)}0000021\phantom{15}\\240000\overline{)51512500}\\\phantom{240000)}\underline{\phantom{}480000\phantom{99}}\\\phantom{240000)9}351250\\\phantom{240000)}\underline{\phantom{9}240000\phantom{9}}\\\phantom{240000)9}1112500\\\end{array}
Use the 8^{th} digit 0 from dividend 51512500
\begin{array}{l}\phantom{240000)}00000214\phantom{16}\\240000\overline{)51512500}\\\phantom{240000)}\underline{\phantom{}480000\phantom{99}}\\\phantom{240000)9}351250\\\phantom{240000)}\underline{\phantom{9}240000\phantom{9}}\\\phantom{240000)9}1112500\\\phantom{240000)}\underline{\phantom{99}960000\phantom{}}\\\phantom{240000)99}152500\\\end{array}
Find closest multiple of 240000 to 1112500. We see that 4 \times 240000 = 960000 is the nearest. Now subtract 960000 from 1112500 to get reminder 152500. Add 4 to quotient.
\text{Quotient: }214 \text{Reminder: }152500
Since 152500 is less than 240000, stop the division. The reminder is 152500. The topmost line 00000214 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 214.
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}