Evaluate
806
Factor
2\times 13\times 31
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\begin{array}{l}\phantom{90)}\phantom{1}\\90\overline{)72540}\\\end{array}
Use the 1^{st} digit 7 from dividend 72540
\begin{array}{l}\phantom{90)}0\phantom{2}\\90\overline{)72540}\\\end{array}
Since 7 is less than 90, use the next digit 2 from dividend 72540 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0\phantom{3}\\90\overline{)72540}\\\end{array}
Use the 2^{nd} digit 2 from dividend 72540
\begin{array}{l}\phantom{90)}00\phantom{4}\\90\overline{)72540}\\\end{array}
Since 72 is less than 90, use the next digit 5 from dividend 72540 and add 0 to the quotient
\begin{array}{l}\phantom{90)}00\phantom{5}\\90\overline{)72540}\\\end{array}
Use the 3^{rd} digit 5 from dividend 72540
\begin{array}{l}\phantom{90)}008\phantom{6}\\90\overline{)72540}\\\phantom{90)}\underline{\phantom{}720\phantom{99}}\\\phantom{90)99}5\\\end{array}
Find closest multiple of 90 to 725. We see that 8 \times 90 = 720 is the nearest. Now subtract 720 from 725 to get reminder 5. Add 8 to quotient.
\begin{array}{l}\phantom{90)}008\phantom{7}\\90\overline{)72540}\\\phantom{90)}\underline{\phantom{}720\phantom{99}}\\\phantom{90)99}54\\\end{array}
Use the 4^{th} digit 4 from dividend 72540
\begin{array}{l}\phantom{90)}0080\phantom{8}\\90\overline{)72540}\\\phantom{90)}\underline{\phantom{}720\phantom{99}}\\\phantom{90)99}54\\\end{array}
Since 54 is less than 90, use the next digit 0 from dividend 72540 and add 0 to the quotient
\begin{array}{l}\phantom{90)}0080\phantom{9}\\90\overline{)72540}\\\phantom{90)}\underline{\phantom{}720\phantom{99}}\\\phantom{90)99}540\\\end{array}
Use the 5^{th} digit 0 from dividend 72540
\begin{array}{l}\phantom{90)}00806\phantom{10}\\90\overline{)72540}\\\phantom{90)}\underline{\phantom{}720\phantom{99}}\\\phantom{90)99}540\\\phantom{90)}\underline{\phantom{99}540\phantom{}}\\\phantom{90)99999}0\\\end{array}
Find closest multiple of 90 to 540. We see that 6 \times 90 = 540 is the nearest. Now subtract 540 from 540 to get reminder 0. Add 6 to quotient.
\text{Quotient: }806 \text{Reminder: }0
Since 0 is less than 90, stop the division. The reminder is 0. The topmost line 00806 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 806.
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}