Evaluate
13
Factor
13
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\begin{array}{l}\phantom{14)}\phantom{1}\\14\overline{)182}\\\end{array}
Use the 1^{st} digit 1 from dividend 182
\begin{array}{l}\phantom{14)}0\phantom{2}\\14\overline{)182}\\\end{array}
Since 1 is less than 14, use the next digit 8 from dividend 182 and add 0 to the quotient
\begin{array}{l}\phantom{14)}0\phantom{3}\\14\overline{)182}\\\end{array}
Use the 2^{nd} digit 8 from dividend 182
\begin{array}{l}\phantom{14)}01\phantom{4}\\14\overline{)182}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)9}4\\\end{array}
Find closest multiple of 14 to 18. We see that 1 \times 14 = 14 is the nearest. Now subtract 14 from 18 to get reminder 4. Add 1 to quotient.
\begin{array}{l}\phantom{14)}01\phantom{5}\\14\overline{)182}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)9}42\\\end{array}
Use the 3^{rd} digit 2 from dividend 182
\begin{array}{l}\phantom{14)}013\phantom{6}\\14\overline{)182}\\\phantom{14)}\underline{\phantom{}14\phantom{9}}\\\phantom{14)9}42\\\phantom{14)}\underline{\phantom{9}42\phantom{}}\\\phantom{14)999}0\\\end{array}
Find closest multiple of 14 to 42. We see that 3 \times 14 = 42 is the nearest. Now subtract 42 from 42 to get reminder 0. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }0
Since 0 is less than 14, 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}