Evaluate
\frac{400000}{53}\approx 7547.169811321
Factor
\frac{2 ^ {7} \cdot 5 ^ {5}}{53} = 7547\frac{9}{53} = 7547.169811320755
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\begin{array}{l}\phantom{106)}\phantom{1}\\106\overline{)800000}\\\end{array}
Use the 1^{st} digit 8 from dividend 800000
\begin{array}{l}\phantom{106)}0\phantom{2}\\106\overline{)800000}\\\end{array}
Since 8 is less than 106, use the next digit 0 from dividend 800000 and add 0 to the quotient
\begin{array}{l}\phantom{106)}0\phantom{3}\\106\overline{)800000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 800000
\begin{array}{l}\phantom{106)}00\phantom{4}\\106\overline{)800000}\\\end{array}
Since 80 is less than 106, use the next digit 0 from dividend 800000 and add 0 to the quotient
\begin{array}{l}\phantom{106)}00\phantom{5}\\106\overline{)800000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 800000
\begin{array}{l}\phantom{106)}007\phantom{6}\\106\overline{)800000}\\\phantom{106)}\underline{\phantom{}742\phantom{999}}\\\phantom{106)9}58\\\end{array}
Find closest multiple of 106 to 800. We see that 7 \times 106 = 742 is the nearest. Now subtract 742 from 800 to get reminder 58. Add 7 to quotient.
\begin{array}{l}\phantom{106)}007\phantom{7}\\106\overline{)800000}\\\phantom{106)}\underline{\phantom{}742\phantom{999}}\\\phantom{106)9}580\\\end{array}
Use the 4^{th} digit 0 from dividend 800000
\begin{array}{l}\phantom{106)}0075\phantom{8}\\106\overline{)800000}\\\phantom{106)}\underline{\phantom{}742\phantom{999}}\\\phantom{106)9}580\\\phantom{106)}\underline{\phantom{9}530\phantom{99}}\\\phantom{106)99}50\\\end{array}
Find closest multiple of 106 to 580. We see that 5 \times 106 = 530 is the nearest. Now subtract 530 from 580 to get reminder 50. Add 5 to quotient.
\begin{array}{l}\phantom{106)}0075\phantom{9}\\106\overline{)800000}\\\phantom{106)}\underline{\phantom{}742\phantom{999}}\\\phantom{106)9}580\\\phantom{106)}\underline{\phantom{9}530\phantom{99}}\\\phantom{106)99}500\\\end{array}
Use the 5^{th} digit 0 from dividend 800000
\begin{array}{l}\phantom{106)}00754\phantom{10}\\106\overline{)800000}\\\phantom{106)}\underline{\phantom{}742\phantom{999}}\\\phantom{106)9}580\\\phantom{106)}\underline{\phantom{9}530\phantom{99}}\\\phantom{106)99}500\\\phantom{106)}\underline{\phantom{99}424\phantom{9}}\\\phantom{106)999}76\\\end{array}
Find closest multiple of 106 to 500. We see that 4 \times 106 = 424 is the nearest. Now subtract 424 from 500 to get reminder 76. Add 4 to quotient.
\begin{array}{l}\phantom{106)}00754\phantom{11}\\106\overline{)800000}\\\phantom{106)}\underline{\phantom{}742\phantom{999}}\\\phantom{106)9}580\\\phantom{106)}\underline{\phantom{9}530\phantom{99}}\\\phantom{106)99}500\\\phantom{106)}\underline{\phantom{99}424\phantom{9}}\\\phantom{106)999}760\\\end{array}
Use the 6^{th} digit 0 from dividend 800000
\begin{array}{l}\phantom{106)}007547\phantom{12}\\106\overline{)800000}\\\phantom{106)}\underline{\phantom{}742\phantom{999}}\\\phantom{106)9}580\\\phantom{106)}\underline{\phantom{9}530\phantom{99}}\\\phantom{106)99}500\\\phantom{106)}\underline{\phantom{99}424\phantom{9}}\\\phantom{106)999}760\\\phantom{106)}\underline{\phantom{999}742\phantom{}}\\\phantom{106)9999}18\\\end{array}
Find closest multiple of 106 to 760. We see that 7 \times 106 = 742 is the nearest. Now subtract 742 from 760 to get reminder 18. Add 7 to quotient.
\text{Quotient: }7547 \text{Reminder: }18
Since 18 is less than 106, stop the division. The reminder is 18. The topmost line 007547 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 7547.
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}