Evaluate
13
Factor
13
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)234}\\\end{array}
Use the 1^{st} digit 2 from dividend 234
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)234}\\\end{array}
Since 2 is less than 18, use the next digit 3 from dividend 234 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)234}\\\end{array}
Use the 2^{nd} digit 3 from dividend 234
\begin{array}{l}\phantom{18)}01\phantom{4}\\18\overline{)234}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}5\\\end{array}
Find closest multiple of 18 to 23. We see that 1 \times 18 = 18 is the nearest. Now subtract 18 from 23 to get reminder 5. Add 1 to quotient.
\begin{array}{l}\phantom{18)}01\phantom{5}\\18\overline{)234}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}54\\\end{array}
Use the 3^{rd} digit 4 from dividend 234
\begin{array}{l}\phantom{18)}013\phantom{6}\\18\overline{)234}\\\phantom{18)}\underline{\phantom{}18\phantom{9}}\\\phantom{18)9}54\\\phantom{18)}\underline{\phantom{9}54\phantom{}}\\\phantom{18)999}0\\\end{array}
Find closest multiple of 18 to 54. We see that 3 \times 18 = 54 is the nearest. Now subtract 54 from 54 to get reminder 0. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }0
Since 0 is less than 18, stop the division. The reminder is 0. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}