Evaluate
42
Factor
2\times 3\times 7
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\begin{array}{l}\phantom{168)}\phantom{1}\\168\overline{)7056}\\\end{array}
Use the 1^{st} digit 7 from dividend 7056
\begin{array}{l}\phantom{168)}0\phantom{2}\\168\overline{)7056}\\\end{array}
Since 7 is less than 168, use the next digit 0 from dividend 7056 and add 0 to the quotient
\begin{array}{l}\phantom{168)}0\phantom{3}\\168\overline{)7056}\\\end{array}
Use the 2^{nd} digit 0 from dividend 7056
\begin{array}{l}\phantom{168)}00\phantom{4}\\168\overline{)7056}\\\end{array}
Since 70 is less than 168, use the next digit 5 from dividend 7056 and add 0 to the quotient
\begin{array}{l}\phantom{168)}00\phantom{5}\\168\overline{)7056}\\\end{array}
Use the 3^{rd} digit 5 from dividend 7056
\begin{array}{l}\phantom{168)}004\phantom{6}\\168\overline{)7056}\\\phantom{168)}\underline{\phantom{}672\phantom{9}}\\\phantom{168)9}33\\\end{array}
Find closest multiple of 168 to 705. We see that 4 \times 168 = 672 is the nearest. Now subtract 672 from 705 to get reminder 33. Add 4 to quotient.
\begin{array}{l}\phantom{168)}004\phantom{7}\\168\overline{)7056}\\\phantom{168)}\underline{\phantom{}672\phantom{9}}\\\phantom{168)9}336\\\end{array}
Use the 4^{th} digit 6 from dividend 7056
\begin{array}{l}\phantom{168)}0042\phantom{8}\\168\overline{)7056}\\\phantom{168)}\underline{\phantom{}672\phantom{9}}\\\phantom{168)9}336\\\phantom{168)}\underline{\phantom{9}336\phantom{}}\\\phantom{168)9999}0\\\end{array}
Find closest multiple of 168 to 336. We see that 2 \times 168 = 336 is the nearest. Now subtract 336 from 336 to get reminder 0. Add 2 to quotient.
\text{Quotient: }42 \text{Reminder: }0
Since 0 is less than 168, stop the division. The reminder is 0. The topmost line 0042 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 42.
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}