Evaluate
20304
Factor
2^{4}\times 3^{3}\times 47
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)223344}\\\end{array}
Use the 1^{st} digit 2 from dividend 223344
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)223344}\\\end{array}
Since 2 is less than 11, use the next digit 2 from dividend 223344 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)223344}\\\end{array}
Use the 2^{nd} digit 2 from dividend 223344
\begin{array}{l}\phantom{11)}02\phantom{4}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}0\\\end{array}
Find closest multiple of 11 to 22. We see that 2 \times 11 = 22 is the nearest. Now subtract 22 from 22 to get reminder 0. Add 2 to quotient.
\begin{array}{l}\phantom{11)}02\phantom{5}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}3\\\end{array}
Use the 3^{rd} digit 3 from dividend 223344
\begin{array}{l}\phantom{11)}020\phantom{6}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}3\\\end{array}
Since 3 is less than 11, use the next digit 3 from dividend 223344 and add 0 to the quotient
\begin{array}{l}\phantom{11)}020\phantom{7}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}33\\\end{array}
Use the 4^{th} digit 3 from dividend 223344
\begin{array}{l}\phantom{11)}0203\phantom{8}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}33\\\phantom{11)}\underline{\phantom{99}33\phantom{99}}\\\phantom{11)9999}0\\\end{array}
Find closest multiple of 11 to 33. We see that 3 \times 11 = 33 is the nearest. Now subtract 33 from 33 to get reminder 0. Add 3 to quotient.
\begin{array}{l}\phantom{11)}0203\phantom{9}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}33\\\phantom{11)}\underline{\phantom{99}33\phantom{99}}\\\phantom{11)9999}4\\\end{array}
Use the 5^{th} digit 4 from dividend 223344
\begin{array}{l}\phantom{11)}02030\phantom{10}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}33\\\phantom{11)}\underline{\phantom{99}33\phantom{99}}\\\phantom{11)9999}4\\\end{array}
Since 4 is less than 11, use the next digit 4 from dividend 223344 and add 0 to the quotient
\begin{array}{l}\phantom{11)}02030\phantom{11}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}33\\\phantom{11)}\underline{\phantom{99}33\phantom{99}}\\\phantom{11)9999}44\\\end{array}
Use the 6^{th} digit 4 from dividend 223344
\begin{array}{l}\phantom{11)}020304\phantom{12}\\11\overline{)223344}\\\phantom{11)}\underline{\phantom{}22\phantom{9999}}\\\phantom{11)99}33\\\phantom{11)}\underline{\phantom{99}33\phantom{99}}\\\phantom{11)9999}44\\\phantom{11)}\underline{\phantom{9999}44\phantom{}}\\\phantom{11)999999}0\\\end{array}
Find closest multiple of 11 to 44. We see that 4 \times 11 = 44 is the nearest. Now subtract 44 from 44 to get reminder 0. Add 4 to quotient.
\text{Quotient: }20304 \text{Reminder: }0
Since 0 is less than 11, stop the division. The reminder is 0. The topmost line 020304 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 20304.
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}