Evaluate
6
Factor
2\times 3
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)126}\\\end{array}
Use the 1^{st} digit 1 from dividend 126
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)126}\\\end{array}
Since 1 is less than 21, use the next digit 2 from dividend 126 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)126}\\\end{array}
Use the 2^{nd} digit 2 from dividend 126
\begin{array}{l}\phantom{21)}00\phantom{4}\\21\overline{)126}\\\end{array}
Since 12 is less than 21, use the next digit 6 from dividend 126 and add 0 to the quotient
\begin{array}{l}\phantom{21)}00\phantom{5}\\21\overline{)126}\\\end{array}
Use the 3^{rd} digit 6 from dividend 126
\begin{array}{l}\phantom{21)}006\phantom{6}\\21\overline{)126}\\\phantom{21)}\underline{\phantom{}126\phantom{}}\\\phantom{21)999}0\\\end{array}
Find closest multiple of 21 to 126. We see that 6 \times 21 = 126 is the nearest. Now subtract 126 from 126 to get reminder 0. Add 6 to quotient.
\text{Quotient: }6 \text{Reminder: }0
Since 0 is less than 21, stop the division. The reminder is 0. The topmost line 006 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6.
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}