Evaluate
13
Factor
13
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\begin{array}{l}\phantom{180)}\phantom{1}\\180\overline{)2340}\\\end{array}
Use the 1^{st} digit 2 from dividend 2340
\begin{array}{l}\phantom{180)}0\phantom{2}\\180\overline{)2340}\\\end{array}
Since 2 is less than 180, use the next digit 3 from dividend 2340 and add 0 to the quotient
\begin{array}{l}\phantom{180)}0\phantom{3}\\180\overline{)2340}\\\end{array}
Use the 2^{nd} digit 3 from dividend 2340
\begin{array}{l}\phantom{180)}00\phantom{4}\\180\overline{)2340}\\\end{array}
Since 23 is less than 180, use the next digit 4 from dividend 2340 and add 0 to the quotient
\begin{array}{l}\phantom{180)}00\phantom{5}\\180\overline{)2340}\\\end{array}
Use the 3^{rd} digit 4 from dividend 2340
\begin{array}{l}\phantom{180)}001\phantom{6}\\180\overline{)2340}\\\phantom{180)}\underline{\phantom{}180\phantom{9}}\\\phantom{180)9}54\\\end{array}
Find closest multiple of 180 to 234. We see that 1 \times 180 = 180 is the nearest. Now subtract 180 from 234 to get reminder 54. Add 1 to quotient.
\begin{array}{l}\phantom{180)}001\phantom{7}\\180\overline{)2340}\\\phantom{180)}\underline{\phantom{}180\phantom{9}}\\\phantom{180)9}540\\\end{array}
Use the 4^{th} digit 0 from dividend 2340
\begin{array}{l}\phantom{180)}0013\phantom{8}\\180\overline{)2340}\\\phantom{180)}\underline{\phantom{}180\phantom{9}}\\\phantom{180)9}540\\\phantom{180)}\underline{\phantom{9}540\phantom{}}\\\phantom{180)9999}0\\\end{array}
Find closest multiple of 180 to 540. We see that 3 \times 180 = 540 is the nearest. Now subtract 540 from 540 to get reminder 0. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }0
Since 0 is less than 180, stop the division. The reminder is 0. The topmost line 0013 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}