Evaluate
\frac{2071}{30}\approx 69.033333333
Factor
\frac{19 \cdot 109}{2 \cdot 3 \cdot 5} = 69\frac{1}{30} = 69.03333333333333
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)6213}\\\end{array}
Use the 1^{st} digit 6 from dividend 6213
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)6213}\\\end{array}
Since 6 is less than 90, use the next digit 2 from dividend 6213 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)6213}\\\end{array}
Use the 2^{nd} digit 2 from dividend 6213
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)6213}\\\end{array}
Since 62 is less than 90, use the next digit 1 from dividend 6213 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)6213}\\\end{array}
Use the 3^{rd} digit 1 from dividend 6213
\begin{array}{l}\phantom{90)}006\phantom{6}\\90\overline{)6213}\\\phantom{90)}\underline{\phantom{}540\phantom{9}}\\\phantom{90)9}81\\\end{array}
Find closest multiple of 90 to 621. We see that 6 \times 90 = 540 is the nearest. Now subtract 540 from 621 to get reminder 81. Add 6 to quotient.
\begin{array}{l}\phantom{90)}006\phantom{7}\\90\overline{)6213}\\\phantom{90)}\underline{\phantom{}540\phantom{9}}\\\phantom{90)9}813\\\end{array}
Use the 4^{th} digit 3 from dividend 6213
\begin{array}{l}\phantom{90)}0069\phantom{8}\\90\overline{)6213}\\\phantom{90)}\underline{\phantom{}540\phantom{9}}\\\phantom{90)9}813\\\phantom{90)}\underline{\phantom{9}810\phantom{}}\\\phantom{90)999}3\\\end{array}
Find closest multiple of 90 to 813. We see that 9 \times 90 = 810 is the nearest. Now subtract 810 from 813 to get reminder 3. Add 9 to quotient.
\text{Quotient: }69 \text{Reminder: }3
Since 3 is less than 90, stop the division. The reminder is 3. The topmost line 0069 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 69.
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}