Evaluate
13
Factor
13
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\begin{array}{l}\phantom{24)}\phantom{1}\\24\overline{)312}\\\end{array}
Use the 1^{st} digit 3 from dividend 312
\begin{array}{l}\phantom{24)}0\phantom{2}\\24\overline{)312}\\\end{array}
Since 3 is less than 24, use the next digit 1 from dividend 312 and add 0 to the quotient
\begin{array}{l}\phantom{24)}0\phantom{3}\\24\overline{)312}\\\end{array}
Use the 2^{nd} digit 1 from dividend 312
\begin{array}{l}\phantom{24)}01\phantom{4}\\24\overline{)312}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}7\\\end{array}
Find closest multiple of 24 to 31. We see that 1 \times 24 = 24 is the nearest. Now subtract 24 from 31 to get reminder 7. Add 1 to quotient.
\begin{array}{l}\phantom{24)}01\phantom{5}\\24\overline{)312}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}72\\\end{array}
Use the 3^{rd} digit 2 from dividend 312
\begin{array}{l}\phantom{24)}013\phantom{6}\\24\overline{)312}\\\phantom{24)}\underline{\phantom{}24\phantom{9}}\\\phantom{24)9}72\\\phantom{24)}\underline{\phantom{9}72\phantom{}}\\\phantom{24)999}0\\\end{array}
Find closest multiple of 24 to 72. We see that 3 \times 24 = 72 is the nearest. Now subtract 72 from 72 to get reminder 0. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }0
Since 0 is less than 24, 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}