Evaluate
23
Factor
23
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\begin{array}{l}\phantom{37)}\phantom{1}\\37\overline{)851}\\\end{array}
Use the 1^{st} digit 8 from dividend 851
\begin{array}{l}\phantom{37)}0\phantom{2}\\37\overline{)851}\\\end{array}
Since 8 is less than 37, use the next digit 5 from dividend 851 and add 0 to the quotient
\begin{array}{l}\phantom{37)}0\phantom{3}\\37\overline{)851}\\\end{array}
Use the 2^{nd} digit 5 from dividend 851
\begin{array}{l}\phantom{37)}02\phantom{4}\\37\overline{)851}\\\phantom{37)}\underline{\phantom{}74\phantom{9}}\\\phantom{37)}11\\\end{array}
Find closest multiple of 37 to 85. We see that 2 \times 37 = 74 is the nearest. Now subtract 74 from 85 to get reminder 11. Add 2 to quotient.
\begin{array}{l}\phantom{37)}02\phantom{5}\\37\overline{)851}\\\phantom{37)}\underline{\phantom{}74\phantom{9}}\\\phantom{37)}111\\\end{array}
Use the 3^{rd} digit 1 from dividend 851
\begin{array}{l}\phantom{37)}023\phantom{6}\\37\overline{)851}\\\phantom{37)}\underline{\phantom{}74\phantom{9}}\\\phantom{37)}111\\\phantom{37)}\underline{\phantom{}111\phantom{}}\\\phantom{37)999}0\\\end{array}
Find closest multiple of 37 to 111. We see that 3 \times 37 = 111 is the nearest. Now subtract 111 from 111 to get reminder 0. Add 3 to quotient.
\text{Quotient: }23 \text{Reminder: }0
Since 0 is less than 37, stop the division. The reminder is 0. The topmost line 023 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 23.
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}