Evaluate
\frac{8656}{21}\approx 412.19047619
Factor
\frac{2 ^ {4} \cdot 541}{3 \cdot 7} = 412\frac{4}{21} = 412.1904761904762
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\begin{array}{l}\phantom{21)}\phantom{1}\\21\overline{)8656}\\\end{array}
Use the 1^{st} digit 8 from dividend 8656
\begin{array}{l}\phantom{21)}0\phantom{2}\\21\overline{)8656}\\\end{array}
Since 8 is less than 21, use the next digit 6 from dividend 8656 and add 0 to the quotient
\begin{array}{l}\phantom{21)}0\phantom{3}\\21\overline{)8656}\\\end{array}
Use the 2^{nd} digit 6 from dividend 8656
\begin{array}{l}\phantom{21)}04\phantom{4}\\21\overline{)8656}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}2\\\end{array}
Find closest multiple of 21 to 86. We see that 4 \times 21 = 84 is the nearest. Now subtract 84 from 86 to get reminder 2. Add 4 to quotient.
\begin{array}{l}\phantom{21)}04\phantom{5}\\21\overline{)8656}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}25\\\end{array}
Use the 3^{rd} digit 5 from dividend 8656
\begin{array}{l}\phantom{21)}041\phantom{6}\\21\overline{)8656}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}25\\\phantom{21)}\underline{\phantom{9}21\phantom{9}}\\\phantom{21)99}4\\\end{array}
Find closest multiple of 21 to 25. We see that 1 \times 21 = 21 is the nearest. Now subtract 21 from 25 to get reminder 4. Add 1 to quotient.
\begin{array}{l}\phantom{21)}041\phantom{7}\\21\overline{)8656}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}25\\\phantom{21)}\underline{\phantom{9}21\phantom{9}}\\\phantom{21)99}46\\\end{array}
Use the 4^{th} digit 6 from dividend 8656
\begin{array}{l}\phantom{21)}0412\phantom{8}\\21\overline{)8656}\\\phantom{21)}\underline{\phantom{}84\phantom{99}}\\\phantom{21)9}25\\\phantom{21)}\underline{\phantom{9}21\phantom{9}}\\\phantom{21)99}46\\\phantom{21)}\underline{\phantom{99}42\phantom{}}\\\phantom{21)999}4\\\end{array}
Find closest multiple of 21 to 46. We see that 2 \times 21 = 42 is the nearest. Now subtract 42 from 46 to get reminder 4. Add 2 to quotient.
\text{Quotient: }412 \text{Reminder: }4
Since 4 is less than 21, stop the division. The reminder is 4. The topmost line 0412 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 412.
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}