Evaluate
6
Factor
2\times 3
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\begin{array}{l}\phantom{114)}\phantom{1}\\114\overline{)684}\\\end{array}
Use the 1^{st} digit 6 from dividend 684
\begin{array}{l}\phantom{114)}0\phantom{2}\\114\overline{)684}\\\end{array}
Since 6 is less than 114, use the next digit 8 from dividend 684 and add 0 to the quotient
\begin{array}{l}\phantom{114)}0\phantom{3}\\114\overline{)684}\\\end{array}
Use the 2^{nd} digit 8 from dividend 684
\begin{array}{l}\phantom{114)}00\phantom{4}\\114\overline{)684}\\\end{array}
Since 68 is less than 114, use the next digit 4 from dividend 684 and add 0 to the quotient
\begin{array}{l}\phantom{114)}00\phantom{5}\\114\overline{)684}\\\end{array}
Use the 3^{rd} digit 4 from dividend 684
\begin{array}{l}\phantom{114)}006\phantom{6}\\114\overline{)684}\\\phantom{114)}\underline{\phantom{}684\phantom{}}\\\phantom{114)999}0\\\end{array}
Find closest multiple of 114 to 684. We see that 6 \times 114 = 684 is the nearest. Now subtract 684 from 684 to get reminder 0. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }0
Since 0 is less than 114, stop the division. The reminder is 0. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}