Evaluate
\frac{625000}{103}\approx 6067.961165049
Factor
\frac{2 ^ {3} \cdot 5 ^ {7}}{103} = 6067\frac{99}{103} = 6067.961165048544
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\begin{array}{l}\phantom{1030)}\phantom{1}\\1030\overline{)6250000}\\\end{array}
Use the 1^{st} digit 6 from dividend 6250000
\begin{array}{l}\phantom{1030)}0\phantom{2}\\1030\overline{)6250000}\\\end{array}
Since 6 is less than 1030, use the next digit 2 from dividend 6250000 and add 0 to the quotient
\begin{array}{l}\phantom{1030)}0\phantom{3}\\1030\overline{)6250000}\\\end{array}
Use the 2^{nd} digit 2 from dividend 6250000
\begin{array}{l}\phantom{1030)}00\phantom{4}\\1030\overline{)6250000}\\\end{array}
Since 62 is less than 1030, use the next digit 5 from dividend 6250000 and add 0 to the quotient
\begin{array}{l}\phantom{1030)}00\phantom{5}\\1030\overline{)6250000}\\\end{array}
Use the 3^{rd} digit 5 from dividend 6250000
\begin{array}{l}\phantom{1030)}000\phantom{6}\\1030\overline{)6250000}\\\end{array}
Since 625 is less than 1030, use the next digit 0 from dividend 6250000 and add 0 to the quotient
\begin{array}{l}\phantom{1030)}000\phantom{7}\\1030\overline{)6250000}\\\end{array}
Use the 4^{th} digit 0 from dividend 6250000
\begin{array}{l}\phantom{1030)}0006\phantom{8}\\1030\overline{)6250000}\\\phantom{1030)}\underline{\phantom{}6180\phantom{999}}\\\phantom{1030)99}70\\\end{array}
Find closest multiple of 1030 to 6250. We see that 6 \times 1030 = 6180 is the nearest. Now subtract 6180 from 6250 to get reminder 70. Add 6 to quotient.
\begin{array}{l}\phantom{1030)}0006\phantom{9}\\1030\overline{)6250000}\\\phantom{1030)}\underline{\phantom{}6180\phantom{999}}\\\phantom{1030)99}700\\\end{array}
Use the 5^{th} digit 0 from dividend 6250000
\begin{array}{l}\phantom{1030)}00060\phantom{10}\\1030\overline{)6250000}\\\phantom{1030)}\underline{\phantom{}6180\phantom{999}}\\\phantom{1030)99}700\\\end{array}
Since 700 is less than 1030, use the next digit 0 from dividend 6250000 and add 0 to the quotient
\begin{array}{l}\phantom{1030)}00060\phantom{11}\\1030\overline{)6250000}\\\phantom{1030)}\underline{\phantom{}6180\phantom{999}}\\\phantom{1030)99}7000\\\end{array}
Use the 6^{th} digit 0 from dividend 6250000
\begin{array}{l}\phantom{1030)}000606\phantom{12}\\1030\overline{)6250000}\\\phantom{1030)}\underline{\phantom{}6180\phantom{999}}\\\phantom{1030)99}7000\\\phantom{1030)}\underline{\phantom{99}6180\phantom{9}}\\\phantom{1030)999}820\\\end{array}
Find closest multiple of 1030 to 7000. We see that 6 \times 1030 = 6180 is the nearest. Now subtract 6180 from 7000 to get reminder 820. Add 6 to quotient.
\begin{array}{l}\phantom{1030)}000606\phantom{13}\\1030\overline{)6250000}\\\phantom{1030)}\underline{\phantom{}6180\phantom{999}}\\\phantom{1030)99}7000\\\phantom{1030)}\underline{\phantom{99}6180\phantom{9}}\\\phantom{1030)999}8200\\\end{array}
Use the 7^{th} digit 0 from dividend 6250000
\begin{array}{l}\phantom{1030)}0006067\phantom{14}\\1030\overline{)6250000}\\\phantom{1030)}\underline{\phantom{}6180\phantom{999}}\\\phantom{1030)99}7000\\\phantom{1030)}\underline{\phantom{99}6180\phantom{9}}\\\phantom{1030)999}8200\\\phantom{1030)}\underline{\phantom{999}7210\phantom{}}\\\phantom{1030)9999}990\\\end{array}
Find closest multiple of 1030 to 8200. We see that 7 \times 1030 = 7210 is the nearest. Now subtract 7210 from 8200 to get reminder 990. Add 7 to quotient.
\text{Quotient: }6067 \text{Reminder: }990
Since 990 is less than 1030, stop the division. The reminder is 990. The topmost line 0006067 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6067.
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}