Evaluate
82
Factor
2\times 41
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\begin{array}{l}\phantom{270)}\phantom{1}\\270\overline{)22140}\\\end{array}
Use the 1^{st} digit 2 from dividend 22140
\begin{array}{l}\phantom{270)}0\phantom{2}\\270\overline{)22140}\\\end{array}
Since 2 is less than 270, use the next digit 2 from dividend 22140 and add 0 to the quotient
\begin{array}{l}\phantom{270)}0\phantom{3}\\270\overline{)22140}\\\end{array}
Use the 2^{nd} digit 2 from dividend 22140
\begin{array}{l}\phantom{270)}00\phantom{4}\\270\overline{)22140}\\\end{array}
Since 22 is less than 270, use the next digit 1 from dividend 22140 and add 0 to the quotient
\begin{array}{l}\phantom{270)}00\phantom{5}\\270\overline{)22140}\\\end{array}
Use the 3^{rd} digit 1 from dividend 22140
\begin{array}{l}\phantom{270)}000\phantom{6}\\270\overline{)22140}\\\end{array}
Since 221 is less than 270, use the next digit 4 from dividend 22140 and add 0 to the quotient
\begin{array}{l}\phantom{270)}000\phantom{7}\\270\overline{)22140}\\\end{array}
Use the 4^{th} digit 4 from dividend 22140
\begin{array}{l}\phantom{270)}0008\phantom{8}\\270\overline{)22140}\\\phantom{270)}\underline{\phantom{}2160\phantom{9}}\\\phantom{270)99}54\\\end{array}
Find closest multiple of 270 to 2214. We see that 8 \times 270 = 2160 is the nearest. Now subtract 2160 from 2214 to get reminder 54. Add 8 to quotient.
\begin{array}{l}\phantom{270)}0008\phantom{9}\\270\overline{)22140}\\\phantom{270)}\underline{\phantom{}2160\phantom{9}}\\\phantom{270)99}540\\\end{array}
Use the 5^{th} digit 0 from dividend 22140
\begin{array}{l}\phantom{270)}00082\phantom{10}\\270\overline{)22140}\\\phantom{270)}\underline{\phantom{}2160\phantom{9}}\\\phantom{270)99}540\\\phantom{270)}\underline{\phantom{99}540\phantom{}}\\\phantom{270)99999}0\\\end{array}
Find closest multiple of 270 to 540. We see that 2 \times 270 = 540 is the nearest. Now subtract 540 from 540 to get reminder 0. Add 2 to quotient.
\text{Quotient: }82 \text{Reminder: }0
Since 0 is less than 270, stop the division. The reminder is 0. The topmost line 00082 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 82.
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}