Evaluate
\frac{20002}{3113}\approx 6.425313203
Factor
\frac{2 \cdot 73 \cdot 137}{11 \cdot 283} = 6\frac{1324}{3113} = 6.425313202698362
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\begin{array}{l}\phantom{3116113)}\phantom{1}\\3116113\overline{)20022002}\\\end{array}
Use the 1^{st} digit 2 from dividend 20022002
\begin{array}{l}\phantom{3116113)}0\phantom{2}\\3116113\overline{)20022002}\\\end{array}
Since 2 is less than 3116113, use the next digit 0 from dividend 20022002 and add 0 to the quotient
\begin{array}{l}\phantom{3116113)}0\phantom{3}\\3116113\overline{)20022002}\\\end{array}
Use the 2^{nd} digit 0 from dividend 20022002
\begin{array}{l}\phantom{3116113)}00\phantom{4}\\3116113\overline{)20022002}\\\end{array}
Since 20 is less than 3116113, use the next digit 0 from dividend 20022002 and add 0 to the quotient
\begin{array}{l}\phantom{3116113)}00\phantom{5}\\3116113\overline{)20022002}\\\end{array}
Use the 3^{rd} digit 0 from dividend 20022002
\begin{array}{l}\phantom{3116113)}000\phantom{6}\\3116113\overline{)20022002}\\\end{array}
Since 200 is less than 3116113, use the next digit 2 from dividend 20022002 and add 0 to the quotient
\begin{array}{l}\phantom{3116113)}000\phantom{7}\\3116113\overline{)20022002}\\\end{array}
Use the 4^{th} digit 2 from dividend 20022002
\begin{array}{l}\phantom{3116113)}0000\phantom{8}\\3116113\overline{)20022002}\\\end{array}
Since 2002 is less than 3116113, use the next digit 2 from dividend 20022002 and add 0 to the quotient
\begin{array}{l}\phantom{3116113)}0000\phantom{9}\\3116113\overline{)20022002}\\\end{array}
Use the 5^{th} digit 2 from dividend 20022002
\begin{array}{l}\phantom{3116113)}00000\phantom{10}\\3116113\overline{)20022002}\\\end{array}
Since 20022 is less than 3116113, use the next digit 0 from dividend 20022002 and add 0 to the quotient
\begin{array}{l}\phantom{3116113)}00000\phantom{11}\\3116113\overline{)20022002}\\\end{array}
Use the 6^{th} digit 0 from dividend 20022002
\begin{array}{l}\phantom{3116113)}000000\phantom{12}\\3116113\overline{)20022002}\\\end{array}
Since 200220 is less than 3116113, use the next digit 0 from dividend 20022002 and add 0 to the quotient
\begin{array}{l}\phantom{3116113)}000000\phantom{13}\\3116113\overline{)20022002}\\\end{array}
Use the 7^{th} digit 0 from dividend 20022002
\begin{array}{l}\phantom{3116113)}0000000\phantom{14}\\3116113\overline{)20022002}\\\end{array}
Since 2002200 is less than 3116113, use the next digit 2 from dividend 20022002 and add 0 to the quotient
\begin{array}{l}\phantom{3116113)}0000000\phantom{15}\\3116113\overline{)20022002}\\\end{array}
Use the 8^{th} digit 2 from dividend 20022002
\begin{array}{l}\phantom{3116113)}00000006\phantom{16}\\3116113\overline{)20022002}\\\phantom{3116113)}\underline{\phantom{}18696678\phantom{}}\\\phantom{3116113)9}1325324\\\end{array}
Find closest multiple of 3116113 to 20022002. We see that 6 \times 3116113 = 18696678 is the nearest. Now subtract 18696678 from 20022002 to get reminder 1325324. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }1325324
Since 1325324 is less than 3116113, stop the division. The reminder is 1325324. The topmost line 00000006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}