Evaluate
82966
Factor
2\times 13\times 3191
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\begin{array}{l}\phantom{22)}\phantom{1}\\22\overline{)1825252}\\\end{array}
Use the 1^{st} digit 1 from dividend 1825252
\begin{array}{l}\phantom{22)}0\phantom{2}\\22\overline{)1825252}\\\end{array}
Since 1 is less than 22, use the next digit 8 from dividend 1825252 and add 0 to the quotient
\begin{array}{l}\phantom{22)}0\phantom{3}\\22\overline{)1825252}\\\end{array}
Use the 2^{nd} digit 8 from dividend 1825252
\begin{array}{l}\phantom{22)}00\phantom{4}\\22\overline{)1825252}\\\end{array}
Since 18 is less than 22, use the next digit 2 from dividend 1825252 and add 0 to the quotient
\begin{array}{l}\phantom{22)}00\phantom{5}\\22\overline{)1825252}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1825252
\begin{array}{l}\phantom{22)}008\phantom{6}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}6\\\end{array}
Find closest multiple of 22 to 182. We see that 8 \times 22 = 176 is the nearest. Now subtract 176 from 182 to get reminder 6. Add 8 to quotient.
\begin{array}{l}\phantom{22)}008\phantom{7}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}65\\\end{array}
Use the 4^{th} digit 5 from dividend 1825252
\begin{array}{l}\phantom{22)}0082\phantom{8}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}65\\\phantom{22)}\underline{\phantom{99}44\phantom{999}}\\\phantom{22)99}21\\\end{array}
Find closest multiple of 22 to 65. We see that 2 \times 22 = 44 is the nearest. Now subtract 44 from 65 to get reminder 21. Add 2 to quotient.
\begin{array}{l}\phantom{22)}0082\phantom{9}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}65\\\phantom{22)}\underline{\phantom{99}44\phantom{999}}\\\phantom{22)99}212\\\end{array}
Use the 5^{th} digit 2 from dividend 1825252
\begin{array}{l}\phantom{22)}00829\phantom{10}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}65\\\phantom{22)}\underline{\phantom{99}44\phantom{999}}\\\phantom{22)99}212\\\phantom{22)}\underline{\phantom{99}198\phantom{99}}\\\phantom{22)999}14\\\end{array}
Find closest multiple of 22 to 212. We see that 9 \times 22 = 198 is the nearest. Now subtract 198 from 212 to get reminder 14. Add 9 to quotient.
\begin{array}{l}\phantom{22)}00829\phantom{11}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}65\\\phantom{22)}\underline{\phantom{99}44\phantom{999}}\\\phantom{22)99}212\\\phantom{22)}\underline{\phantom{99}198\phantom{99}}\\\phantom{22)999}145\\\end{array}
Use the 6^{th} digit 5 from dividend 1825252
\begin{array}{l}\phantom{22)}008296\phantom{12}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}65\\\phantom{22)}\underline{\phantom{99}44\phantom{999}}\\\phantom{22)99}212\\\phantom{22)}\underline{\phantom{99}198\phantom{99}}\\\phantom{22)999}145\\\phantom{22)}\underline{\phantom{999}132\phantom{9}}\\\phantom{22)9999}13\\\end{array}
Find closest multiple of 22 to 145. We see that 6 \times 22 = 132 is the nearest. Now subtract 132 from 145 to get reminder 13. Add 6 to quotient.
\begin{array}{l}\phantom{22)}008296\phantom{13}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}65\\\phantom{22)}\underline{\phantom{99}44\phantom{999}}\\\phantom{22)99}212\\\phantom{22)}\underline{\phantom{99}198\phantom{99}}\\\phantom{22)999}145\\\phantom{22)}\underline{\phantom{999}132\phantom{9}}\\\phantom{22)9999}132\\\end{array}
Use the 7^{th} digit 2 from dividend 1825252
\begin{array}{l}\phantom{22)}0082966\phantom{14}\\22\overline{)1825252}\\\phantom{22)}\underline{\phantom{}176\phantom{9999}}\\\phantom{22)99}65\\\phantom{22)}\underline{\phantom{99}44\phantom{999}}\\\phantom{22)99}212\\\phantom{22)}\underline{\phantom{99}198\phantom{99}}\\\phantom{22)999}145\\\phantom{22)}\underline{\phantom{999}132\phantom{9}}\\\phantom{22)9999}132\\\phantom{22)}\underline{\phantom{9999}132\phantom{}}\\\phantom{22)9999999}0\\\end{array}
Find closest multiple of 22 to 132. We see that 6 \times 22 = 132 is the nearest. Now subtract 132 from 132 to get reminder 0. Add 6 to quotient.
\text{Quotient: }82966 \text{Reminder: }0
Since 0 is less than 22, stop the division. The reminder is 0. The topmost line 0082966 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 82966.
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}