Evaluate
3
Factor
3
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\begin{array}{l}\phantom{54)}\phantom{1}\\54\overline{)162}\\\end{array}
Use the 1^{st} digit 1 from dividend 162
\begin{array}{l}\phantom{54)}0\phantom{2}\\54\overline{)162}\\\end{array}
Since 1 is less than 54, use the next digit 6 from dividend 162 and add 0 to the quotient
\begin{array}{l}\phantom{54)}0\phantom{3}\\54\overline{)162}\\\end{array}
Use the 2^{nd} digit 6 from dividend 162
\begin{array}{l}\phantom{54)}00\phantom{4}\\54\overline{)162}\\\end{array}
Since 16 is less than 54, use the next digit 2 from dividend 162 and add 0 to the quotient
\begin{array}{l}\phantom{54)}00\phantom{5}\\54\overline{)162}\\\end{array}
Use the 3^{rd} digit 2 from dividend 162
\begin{array}{l}\phantom{54)}003\phantom{6}\\54\overline{)162}\\\phantom{54)}\underline{\phantom{}162\phantom{}}\\\phantom{54)999}0\\\end{array}
Find closest multiple of 54 to 162. We see that 3 \times 54 = 162 is the nearest. Now subtract 162 from 162 to get reminder 0. Add 3 to quotient.
\text{Quotient: }3 \text{Reminder: }0
Since 0 is less than 54, stop the division. The reminder is 0. The topmost line 003 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.
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}