Evaluate
\frac{89442719}{20000}=4472.13595
Factor
\frac{31 \cdot 2885249}{2 ^ {5} \cdot 5 ^ {4}} = 4472\frac{2719}{20000} = 4472.13595
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\begin{array}{l}\phantom{20000)}\phantom{1}\\20000\overline{)89442719}\\\end{array}
Use the 1^{st} digit 8 from dividend 89442719
\begin{array}{l}\phantom{20000)}0\phantom{2}\\20000\overline{)89442719}\\\end{array}
Since 8 is less than 20000, use the next digit 9 from dividend 89442719 and add 0 to the quotient
\begin{array}{l}\phantom{20000)}0\phantom{3}\\20000\overline{)89442719}\\\end{array}
Use the 2^{nd} digit 9 from dividend 89442719
\begin{array}{l}\phantom{20000)}00\phantom{4}\\20000\overline{)89442719}\\\end{array}
Since 89 is less than 20000, use the next digit 4 from dividend 89442719 and add 0 to the quotient
\begin{array}{l}\phantom{20000)}00\phantom{5}\\20000\overline{)89442719}\\\end{array}
Use the 3^{rd} digit 4 from dividend 89442719
\begin{array}{l}\phantom{20000)}000\phantom{6}\\20000\overline{)89442719}\\\end{array}
Since 894 is less than 20000, use the next digit 4 from dividend 89442719 and add 0 to the quotient
\begin{array}{l}\phantom{20000)}000\phantom{7}\\20000\overline{)89442719}\\\end{array}
Use the 4^{th} digit 4 from dividend 89442719
\begin{array}{l}\phantom{20000)}0000\phantom{8}\\20000\overline{)89442719}\\\end{array}
Since 8944 is less than 20000, use the next digit 2 from dividend 89442719 and add 0 to the quotient
\begin{array}{l}\phantom{20000)}0000\phantom{9}\\20000\overline{)89442719}\\\end{array}
Use the 5^{th} digit 2 from dividend 89442719
\begin{array}{l}\phantom{20000)}00004\phantom{10}\\20000\overline{)89442719}\\\phantom{20000)}\underline{\phantom{}80000\phantom{999}}\\\phantom{20000)9}9442\\\end{array}
Find closest multiple of 20000 to 89442. We see that 4 \times 20000 = 80000 is the nearest. Now subtract 80000 from 89442 to get reminder 9442. Add 4 to quotient.
\begin{array}{l}\phantom{20000)}00004\phantom{11}\\20000\overline{)89442719}\\\phantom{20000)}\underline{\phantom{}80000\phantom{999}}\\\phantom{20000)9}94427\\\end{array}
Use the 6^{th} digit 7 from dividend 89442719
\begin{array}{l}\phantom{20000)}000044\phantom{12}\\20000\overline{)89442719}\\\phantom{20000)}\underline{\phantom{}80000\phantom{999}}\\\phantom{20000)9}94427\\\phantom{20000)}\underline{\phantom{9}80000\phantom{99}}\\\phantom{20000)9}14427\\\end{array}
Find closest multiple of 20000 to 94427. We see that 4 \times 20000 = 80000 is the nearest. Now subtract 80000 from 94427 to get reminder 14427. Add 4 to quotient.
\begin{array}{l}\phantom{20000)}000044\phantom{13}\\20000\overline{)89442719}\\\phantom{20000)}\underline{\phantom{}80000\phantom{999}}\\\phantom{20000)9}94427\\\phantom{20000)}\underline{\phantom{9}80000\phantom{99}}\\\phantom{20000)9}144271\\\end{array}
Use the 7^{th} digit 1 from dividend 89442719
\begin{array}{l}\phantom{20000)}0000447\phantom{14}\\20000\overline{)89442719}\\\phantom{20000)}\underline{\phantom{}80000\phantom{999}}\\\phantom{20000)9}94427\\\phantom{20000)}\underline{\phantom{9}80000\phantom{99}}\\\phantom{20000)9}144271\\\phantom{20000)}\underline{\phantom{9}140000\phantom{9}}\\\phantom{20000)999}4271\\\end{array}
Find closest multiple of 20000 to 144271. We see that 7 \times 20000 = 140000 is the nearest. Now subtract 140000 from 144271 to get reminder 4271. Add 7 to quotient.
\begin{array}{l}\phantom{20000)}0000447\phantom{15}\\20000\overline{)89442719}\\\phantom{20000)}\underline{\phantom{}80000\phantom{999}}\\\phantom{20000)9}94427\\\phantom{20000)}\underline{\phantom{9}80000\phantom{99}}\\\phantom{20000)9}144271\\\phantom{20000)}\underline{\phantom{9}140000\phantom{9}}\\\phantom{20000)999}42719\\\end{array}
Use the 8^{th} digit 9 from dividend 89442719
\begin{array}{l}\phantom{20000)}00004472\phantom{16}\\20000\overline{)89442719}\\\phantom{20000)}\underline{\phantom{}80000\phantom{999}}\\\phantom{20000)9}94427\\\phantom{20000)}\underline{\phantom{9}80000\phantom{99}}\\\phantom{20000)9}144271\\\phantom{20000)}\underline{\phantom{9}140000\phantom{9}}\\\phantom{20000)999}42719\\\phantom{20000)}\underline{\phantom{999}40000\phantom{}}\\\phantom{20000)9999}2719\\\end{array}
Find closest multiple of 20000 to 42719. We see that 2 \times 20000 = 40000 is the nearest. Now subtract 40000 from 42719 to get reminder 2719. Add 2 to quotient.
\text{Quotient: }4472 \text{Reminder: }2719
Since 2719 is less than 20000, stop the division. The reminder is 2719. The topmost line 00004472 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4472.
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}