Evaluate
21
Factor
3\times 7
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)441}\\\end{array}
Use the 1^{st} digit 4 from dividend 441
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)441}\\\end{array}
Since 4 is less than 21, use the next digit 4 from dividend 441 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)441}\\\end{array}
Use the 2^{nd} digit 4 from dividend 441
\begin{array}{l}\phantom{21)}02\phantom{4}\\21\overline{)441}\\\phantom{21)}\underline{\phantom{}42\phantom{9}}\\\phantom{21)9}2\\\end{array}
Find closest multiple of 21 to 44. We see that 2 \times 21 = 42 is the nearest. Now subtract 42 from 44 to get reminder 2. Add 2 to quotient.
\begin{array}{l}\phantom{21)}02\phantom{5}\\21\overline{)441}\\\phantom{21)}\underline{\phantom{}42\phantom{9}}\\\phantom{21)9}21\\\end{array}
Use the 3^{rd} digit 1 from dividend 441
\begin{array}{l}\phantom{21)}021\phantom{6}\\21\overline{)441}\\\phantom{21)}\underline{\phantom{}42\phantom{9}}\\\phantom{21)9}21\\\phantom{21)}\underline{\phantom{9}21\phantom{}}\\\phantom{21)999}0\\\end{array}
Find closest multiple of 21 to 21. We see that 1 \times 21 = 21 is the nearest. Now subtract 21 from 21 to get reminder 0. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }0
Since 0 is less than 21, stop the division. The reminder is 0. The topmost line 021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}