Evaluate
1010101
Factor
73\times 101\times 137
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)22222222}\\\end{array}
Use the 1^{st} digit 2 from dividend 22222222
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)22222222}\\\end{array}
Since 2 is less than 22, use the next digit 2 from dividend 22222222 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)22222222}\\\end{array}
Use the 2^{nd} digit 2 from dividend 22222222
\begin{array}{l}\phantom{22)}01\phantom{4}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}0\\\end{array}
Find closest multiple of 22 to 22. We see that 1 \times 22 = 22 is the nearest. Now subtract 22 from 22 to get reminder 0. Add 1 to quotient.
\begin{array}{l}\phantom{22)}01\phantom{5}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}2\\\end{array}
Use the 3^{rd} digit 2 from dividend 22222222
\begin{array}{l}\phantom{22)}010\phantom{6}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}2\\\end{array}
Since 2 is less than 22, use the next digit 2 from dividend 22222222 and add 0 to the quotient
\begin{array}{l}\phantom{22)}010\phantom{7}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\end{array}
Use the 4^{th} digit 2 from dividend 22222222
\begin{array}{l}\phantom{22)}0101\phantom{8}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}0\\\end{array}
Find closest multiple of 22 to 22. We see that 1 \times 22 = 22 is the nearest. Now subtract 22 from 22 to get reminder 0. Add 1 to quotient.
\begin{array}{l}\phantom{22)}0101\phantom{9}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}2\\\end{array}
Use the 5^{th} digit 2 from dividend 22222222
\begin{array}{l}\phantom{22)}01010\phantom{10}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}2\\\end{array}
Since 2 is less than 22, use the next digit 2 from dividend 22222222 and add 0 to the quotient
\begin{array}{l}\phantom{22)}01010\phantom{11}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}22\\\end{array}
Use the 6^{th} digit 2 from dividend 22222222
\begin{array}{l}\phantom{22)}010101\phantom{12}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}22\\\phantom{22)}\underline{\phantom{9999}22\phantom{99}}\\\phantom{22)999999}0\\\end{array}
Find closest multiple of 22 to 22. We see that 1 \times 22 = 22 is the nearest. Now subtract 22 from 22 to get reminder 0. Add 1 to quotient.
\begin{array}{l}\phantom{22)}010101\phantom{13}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}22\\\phantom{22)}\underline{\phantom{9999}22\phantom{99}}\\\phantom{22)999999}2\\\end{array}
Use the 7^{th} digit 2 from dividend 22222222
\begin{array}{l}\phantom{22)}0101010\phantom{14}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}22\\\phantom{22)}\underline{\phantom{9999}22\phantom{99}}\\\phantom{22)999999}2\\\end{array}
Since 2 is less than 22, use the next digit 2 from dividend 22222222 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0101010\phantom{15}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}22\\\phantom{22)}\underline{\phantom{9999}22\phantom{99}}\\\phantom{22)999999}22\\\end{array}
Use the 8^{th} digit 2 from dividend 22222222
\begin{array}{l}\phantom{22)}01010101\phantom{16}\\22\overline{)22222222}\\\phantom{22)}\underline{\phantom{}22\phantom{999999}}\\\phantom{22)99}22\\\phantom{22)}\underline{\phantom{99}22\phantom{9999}}\\\phantom{22)9999}22\\\phantom{22)}\underline{\phantom{9999}22\phantom{99}}\\\phantom{22)999999}22\\\phantom{22)}\underline{\phantom{999999}22\phantom{}}\\\phantom{22)99999999}0\\\end{array}
Find closest multiple of 22 to 22. We see that 1 \times 22 = 22 is the nearest. Now subtract 22 from 22 to get reminder 0. Add 1 to quotient.
\text{Quotient: }1010101 \text{Reminder: }0
Since 0 is less than 22, stop the division. The reminder is 0. The topmost line 01010101 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1010101.
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}