Evaluate
\frac{220000}{7}\approx 31428.571428571
Factor
\frac{2 ^ {5} \cdot 5 ^ {4} \cdot 11}{7} = 31428\frac{4}{7} = 31428.571428571428
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\begin{array}{l}\phantom{42)}\phantom{1}\\42\overline{)1320000}\\\end{array}
Use the 1^{st} digit 1 from dividend 1320000
\begin{array}{l}\phantom{42)}0\phantom{2}\\42\overline{)1320000}\\\end{array}
Since 1 is less than 42, use the next digit 3 from dividend 1320000 and add 0 to the quotient
\begin{array}{l}\phantom{42)}0\phantom{3}\\42\overline{)1320000}\\\end{array}
Use the 2^{nd} digit 3 from dividend 1320000
\begin{array}{l}\phantom{42)}00\phantom{4}\\42\overline{)1320000}\\\end{array}
Since 13 is less than 42, use the next digit 2 from dividend 1320000 and add 0 to the quotient
\begin{array}{l}\phantom{42)}00\phantom{5}\\42\overline{)1320000}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1320000
\begin{array}{l}\phantom{42)}003\phantom{6}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}6\\\end{array}
Find closest multiple of 42 to 132. We see that 3 \times 42 = 126 is the nearest. Now subtract 126 from 132 to get reminder 6. Add 3 to quotient.
\begin{array}{l}\phantom{42)}003\phantom{7}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}60\\\end{array}
Use the 4^{th} digit 0 from dividend 1320000
\begin{array}{l}\phantom{42)}0031\phantom{8}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}60\\\phantom{42)}\underline{\phantom{99}42\phantom{999}}\\\phantom{42)99}18\\\end{array}
Find closest multiple of 42 to 60. We see that 1 \times 42 = 42 is the nearest. Now subtract 42 from 60 to get reminder 18. Add 1 to quotient.
\begin{array}{l}\phantom{42)}0031\phantom{9}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}60\\\phantom{42)}\underline{\phantom{99}42\phantom{999}}\\\phantom{42)99}180\\\end{array}
Use the 5^{th} digit 0 from dividend 1320000
\begin{array}{l}\phantom{42)}00314\phantom{10}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}60\\\phantom{42)}\underline{\phantom{99}42\phantom{999}}\\\phantom{42)99}180\\\phantom{42)}\underline{\phantom{99}168\phantom{99}}\\\phantom{42)999}12\\\end{array}
Find closest multiple of 42 to 180. We see that 4 \times 42 = 168 is the nearest. Now subtract 168 from 180 to get reminder 12. Add 4 to quotient.
\begin{array}{l}\phantom{42)}00314\phantom{11}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}60\\\phantom{42)}\underline{\phantom{99}42\phantom{999}}\\\phantom{42)99}180\\\phantom{42)}\underline{\phantom{99}168\phantom{99}}\\\phantom{42)999}120\\\end{array}
Use the 6^{th} digit 0 from dividend 1320000
\begin{array}{l}\phantom{42)}003142\phantom{12}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}60\\\phantom{42)}\underline{\phantom{99}42\phantom{999}}\\\phantom{42)99}180\\\phantom{42)}\underline{\phantom{99}168\phantom{99}}\\\phantom{42)999}120\\\phantom{42)}\underline{\phantom{9999}84\phantom{9}}\\\phantom{42)9999}36\\\end{array}
Find closest multiple of 42 to 120. We see that 2 \times 42 = 84 is the nearest. Now subtract 84 from 120 to get reminder 36. Add 2 to quotient.
\begin{array}{l}\phantom{42)}003142\phantom{13}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}60\\\phantom{42)}\underline{\phantom{99}42\phantom{999}}\\\phantom{42)99}180\\\phantom{42)}\underline{\phantom{99}168\phantom{99}}\\\phantom{42)999}120\\\phantom{42)}\underline{\phantom{9999}84\phantom{9}}\\\phantom{42)9999}360\\\end{array}
Use the 7^{th} digit 0 from dividend 1320000
\begin{array}{l}\phantom{42)}0031428\phantom{14}\\42\overline{)1320000}\\\phantom{42)}\underline{\phantom{}126\phantom{9999}}\\\phantom{42)99}60\\\phantom{42)}\underline{\phantom{99}42\phantom{999}}\\\phantom{42)99}180\\\phantom{42)}\underline{\phantom{99}168\phantom{99}}\\\phantom{42)999}120\\\phantom{42)}\underline{\phantom{9999}84\phantom{9}}\\\phantom{42)9999}360\\\phantom{42)}\underline{\phantom{9999}336\phantom{}}\\\phantom{42)99999}24\\\end{array}
Find closest multiple of 42 to 360. We see that 8 \times 42 = 336 is the nearest. Now subtract 336 from 360 to get reminder 24. Add 8 to quotient.
\text{Quotient: }31428 \text{Reminder: }24
Since 24 is less than 42, stop the division. The reminder is 24. The topmost line 0031428 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 31428.
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}