Evaluate
\frac{123456}{4321}\approx 28.571164082
Factor
\frac{2 ^ {6} \cdot 3 \cdot 643}{29 \cdot 149} = 28\frac{2468}{4321} = 28.571164082388336
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\begin{array}{l}\phantom{4321)}\phantom{1}\\4321\overline{)123456}\\\end{array}
Use the 1^{st} digit 1 from dividend 123456
\begin{array}{l}\phantom{4321)}0\phantom{2}\\4321\overline{)123456}\\\end{array}
Since 1 is less than 4321, use the next digit 2 from dividend 123456 and add 0 to the quotient
\begin{array}{l}\phantom{4321)}0\phantom{3}\\4321\overline{)123456}\\\end{array}
Use the 2^{nd} digit 2 from dividend 123456
\begin{array}{l}\phantom{4321)}00\phantom{4}\\4321\overline{)123456}\\\end{array}
Since 12 is less than 4321, use the next digit 3 from dividend 123456 and add 0 to the quotient
\begin{array}{l}\phantom{4321)}00\phantom{5}\\4321\overline{)123456}\\\end{array}
Use the 3^{rd} digit 3 from dividend 123456
\begin{array}{l}\phantom{4321)}000\phantom{6}\\4321\overline{)123456}\\\end{array}
Since 123 is less than 4321, use the next digit 4 from dividend 123456 and add 0 to the quotient
\begin{array}{l}\phantom{4321)}000\phantom{7}\\4321\overline{)123456}\\\end{array}
Use the 4^{th} digit 4 from dividend 123456
\begin{array}{l}\phantom{4321)}0000\phantom{8}\\4321\overline{)123456}\\\end{array}
Since 1234 is less than 4321, use the next digit 5 from dividend 123456 and add 0 to the quotient
\begin{array}{l}\phantom{4321)}0000\phantom{9}\\4321\overline{)123456}\\\end{array}
Use the 5^{th} digit 5 from dividend 123456
\begin{array}{l}\phantom{4321)}00002\phantom{10}\\4321\overline{)123456}\\\phantom{4321)}\underline{\phantom{9}8642\phantom{9}}\\\phantom{4321)9}3703\\\end{array}
Find closest multiple of 4321 to 12345. We see that 2 \times 4321 = 8642 is the nearest. Now subtract 8642 from 12345 to get reminder 3703. Add 2 to quotient.
\begin{array}{l}\phantom{4321)}00002\phantom{11}\\4321\overline{)123456}\\\phantom{4321)}\underline{\phantom{9}8642\phantom{9}}\\\phantom{4321)9}37036\\\end{array}
Use the 6^{th} digit 6 from dividend 123456
\begin{array}{l}\phantom{4321)}000028\phantom{12}\\4321\overline{)123456}\\\phantom{4321)}\underline{\phantom{9}8642\phantom{9}}\\\phantom{4321)9}37036\\\phantom{4321)}\underline{\phantom{9}34568\phantom{}}\\\phantom{4321)99}2468\\\end{array}
Find closest multiple of 4321 to 37036. We see that 8 \times 4321 = 34568 is the nearest. Now subtract 34568 from 37036 to get reminder 2468. Add 8 to quotient.
\text{Quotient: }28 \text{Reminder: }2468
Since 2468 is less than 4321, stop the division. The reminder is 2468. The topmost line 000028 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 28.
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}