Evaluate
\frac{67101}{21589}\approx 3.108110612
Factor
\frac{3 \cdot 22367}{21589} = 3\frac{2334}{21589} = 3.1081106118856825
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\begin{array}{l}\phantom{21589)}\phantom{1}\\21589\overline{)67101}\\\end{array}
Use the 1^{st} digit 6 from dividend 67101
\begin{array}{l}\phantom{21589)}0\phantom{2}\\21589\overline{)67101}\\\end{array}
Since 6 is less than 21589, use the next digit 7 from dividend 67101 and add 0 to the quotient
\begin{array}{l}\phantom{21589)}0\phantom{3}\\21589\overline{)67101}\\\end{array}
Use the 2^{nd} digit 7 from dividend 67101
\begin{array}{l}\phantom{21589)}00\phantom{4}\\21589\overline{)67101}\\\end{array}
Since 67 is less than 21589, use the next digit 1 from dividend 67101 and add 0 to the quotient
\begin{array}{l}\phantom{21589)}00\phantom{5}\\21589\overline{)67101}\\\end{array}
Use the 3^{rd} digit 1 from dividend 67101
\begin{array}{l}\phantom{21589)}000\phantom{6}\\21589\overline{)67101}\\\end{array}
Since 671 is less than 21589, use the next digit 0 from dividend 67101 and add 0 to the quotient
\begin{array}{l}\phantom{21589)}000\phantom{7}\\21589\overline{)67101}\\\end{array}
Use the 4^{th} digit 0 from dividend 67101
\begin{array}{l}\phantom{21589)}0000\phantom{8}\\21589\overline{)67101}\\\end{array}
Since 6710 is less than 21589, use the next digit 1 from dividend 67101 and add 0 to the quotient
\begin{array}{l}\phantom{21589)}0000\phantom{9}\\21589\overline{)67101}\\\end{array}
Use the 5^{th} digit 1 from dividend 67101
\begin{array}{l}\phantom{21589)}00003\phantom{10}\\21589\overline{)67101}\\\phantom{21589)}\underline{\phantom{}64767\phantom{}}\\\phantom{21589)9}2334\\\end{array}
Find closest multiple of 21589 to 67101. We see that 3 \times 21589 = 64767 is the nearest. Now subtract 64767 from 67101 to get reminder 2334. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }2334
Since 2334 is less than 21589, stop the division. The reminder is 2334. The topmost line 00003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}