Evaluate
19
Factor
19
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)342}\\\end{array}
Use the 1^{st} digit 3 from dividend 342
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)342}\\\end{array}
Since 3 is less than 18, use the next digit 4 from dividend 342 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)342}\\\end{array}
Use the 2^{nd} digit 4 from dividend 342
\begin{array}{l}\phantom{18)}01\phantom{4}\\18\overline{)342}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)}16\\\end{array}
Find closest multiple of 18 to 34. We see that 1 \times 18 = 18 is the nearest. Now subtract 18 from 34 to get reminder 16. Add 1 to quotient.
\begin{array}{l}\phantom{18)}01\phantom{5}\\18\overline{)342}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)}162\\\end{array}
Use the 3^{rd} digit 2 from dividend 342
\begin{array}{l}\phantom{18)}019\phantom{6}\\18\overline{)342}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)}162\\\phantom{18)}\underline{\phantom{}162\phantom{}}\\\phantom{18)999}0\\\end{array}
Find closest multiple of 18 to 162. We see that 9 \times 18 = 162 is the nearest. Now subtract 162 from 162 to get reminder 0. Add 9 to quotient.
\text{Quotient: }19 \text{Reminder: }0
Since 0 is less than 18, stop the division. The reminder is 0. The topmost line 019 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 19.
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}