Evaluate
23
Factor
23
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\begin{array}{l}\phantom{197)}\phantom{1}\\197\overline{)4531}\\\end{array}
Use the 1^{st} digit 4 from dividend 4531
\begin{array}{l}\phantom{197)}0\phantom{2}\\197\overline{)4531}\\\end{array}
Since 4 is less than 197, use the next digit 5 from dividend 4531 and add 0 to the quotient
\begin{array}{l}\phantom{197)}0\phantom{3}\\197\overline{)4531}\\\end{array}
Use the 2^{nd} digit 5 from dividend 4531
\begin{array}{l}\phantom{197)}00\phantom{4}\\197\overline{)4531}\\\end{array}
Since 45 is less than 197, use the next digit 3 from dividend 4531 and add 0 to the quotient
\begin{array}{l}\phantom{197)}00\phantom{5}\\197\overline{)4531}\\\end{array}
Use the 3^{rd} digit 3 from dividend 4531
\begin{array}{l}\phantom{197)}002\phantom{6}\\197\overline{)4531}\\\phantom{197)}\underline{\phantom{}394\phantom{9}}\\\phantom{197)9}59\\\end{array}
Find closest multiple of 197 to 453. We see that 2 \times 197 = 394 is the nearest. Now subtract 394 from 453 to get reminder 59. Add 2 to quotient.
\begin{array}{l}\phantom{197)}002\phantom{7}\\197\overline{)4531}\\\phantom{197)}\underline{\phantom{}394\phantom{9}}\\\phantom{197)9}591\\\end{array}
Use the 4^{th} digit 1 from dividend 4531
\begin{array}{l}\phantom{197)}0023\phantom{8}\\197\overline{)4531}\\\phantom{197)}\underline{\phantom{}394\phantom{9}}\\\phantom{197)9}591\\\phantom{197)}\underline{\phantom{9}591\phantom{}}\\\phantom{197)9999}0\\\end{array}
Find closest multiple of 197 to 591. We see that 3 \times 197 = 591 is the nearest. Now subtract 591 from 591 to get reminder 0. Add 3 to quotient.
\text{Quotient: }23 \text{Reminder: }0
Since 0 is less than 197, stop the division. The reminder is 0. The topmost line 0023 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}