Evaluate
\frac{14606927}{11}\approx 1327902.454545455
Factor
\frac{17 ^ {2} \cdot 50543}{11} = 1327902\frac{5}{11} = 1327902.4545454546
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\begin{array}{l}\phantom{66)}\phantom{1}\\66\overline{)87641562}\\\end{array}
Use the 1^{st} digit 8 from dividend 87641562
\begin{array}{l}\phantom{66)}0\phantom{2}\\66\overline{)87641562}\\\end{array}
Since 8 is less than 66, use the next digit 7 from dividend 87641562 and add 0 to the quotient
\begin{array}{l}\phantom{66)}0\phantom{3}\\66\overline{)87641562}\\\end{array}
Use the 2^{nd} digit 7 from dividend 87641562
\begin{array}{l}\phantom{66)}01\phantom{4}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}21\\\end{array}
Find closest multiple of 66 to 87. We see that 1 \times 66 = 66 is the nearest. Now subtract 66 from 87 to get reminder 21. Add 1 to quotient.
\begin{array}{l}\phantom{66)}01\phantom{5}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\end{array}
Use the 3^{rd} digit 6 from dividend 87641562
\begin{array}{l}\phantom{66)}013\phantom{6}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}18\\\end{array}
Find closest multiple of 66 to 216. We see that 3 \times 66 = 198 is the nearest. Now subtract 198 from 216 to get reminder 18. Add 3 to quotient.
\begin{array}{l}\phantom{66)}013\phantom{7}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\end{array}
Use the 4^{th} digit 4 from dividend 87641562
\begin{array}{l}\phantom{66)}0132\phantom{8}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}52\\\end{array}
Find closest multiple of 66 to 184. We see that 2 \times 66 = 132 is the nearest. Now subtract 132 from 184 to get reminder 52. Add 2 to quotient.
\begin{array}{l}\phantom{66)}0132\phantom{9}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}521\\\end{array}
Use the 5^{th} digit 1 from dividend 87641562
\begin{array}{l}\phantom{66)}01327\phantom{10}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}521\\\phantom{66)}\underline{\phantom{99}462\phantom{999}}\\\phantom{66)999}59\\\end{array}
Find closest multiple of 66 to 521. We see that 7 \times 66 = 462 is the nearest. Now subtract 462 from 521 to get reminder 59. Add 7 to quotient.
\begin{array}{l}\phantom{66)}01327\phantom{11}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}521\\\phantom{66)}\underline{\phantom{99}462\phantom{999}}\\\phantom{66)999}595\\\end{array}
Use the 6^{th} digit 5 from dividend 87641562
\begin{array}{l}\phantom{66)}013279\phantom{12}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}521\\\phantom{66)}\underline{\phantom{99}462\phantom{999}}\\\phantom{66)999}595\\\phantom{66)}\underline{\phantom{999}594\phantom{99}}\\\phantom{66)99999}1\\\end{array}
Find closest multiple of 66 to 595. We see that 9 \times 66 = 594 is the nearest. Now subtract 594 from 595 to get reminder 1. Add 9 to quotient.
\begin{array}{l}\phantom{66)}013279\phantom{13}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}521\\\phantom{66)}\underline{\phantom{99}462\phantom{999}}\\\phantom{66)999}595\\\phantom{66)}\underline{\phantom{999}594\phantom{99}}\\\phantom{66)99999}16\\\end{array}
Use the 7^{th} digit 6 from dividend 87641562
\begin{array}{l}\phantom{66)}0132790\phantom{14}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}521\\\phantom{66)}\underline{\phantom{99}462\phantom{999}}\\\phantom{66)999}595\\\phantom{66)}\underline{\phantom{999}594\phantom{99}}\\\phantom{66)99999}16\\\end{array}
Since 16 is less than 66, use the next digit 2 from dividend 87641562 and add 0 to the quotient
\begin{array}{l}\phantom{66)}0132790\phantom{15}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}521\\\phantom{66)}\underline{\phantom{99}462\phantom{999}}\\\phantom{66)999}595\\\phantom{66)}\underline{\phantom{999}594\phantom{99}}\\\phantom{66)99999}162\\\end{array}
Use the 8^{th} digit 2 from dividend 87641562
\begin{array}{l}\phantom{66)}01327902\phantom{16}\\66\overline{)87641562}\\\phantom{66)}\underline{\phantom{}66\phantom{999999}}\\\phantom{66)}216\\\phantom{66)}\underline{\phantom{}198\phantom{99999}}\\\phantom{66)9}184\\\phantom{66)}\underline{\phantom{9}132\phantom{9999}}\\\phantom{66)99}521\\\phantom{66)}\underline{\phantom{99}462\phantom{999}}\\\phantom{66)999}595\\\phantom{66)}\underline{\phantom{999}594\phantom{99}}\\\phantom{66)99999}162\\\phantom{66)}\underline{\phantom{99999}132\phantom{}}\\\phantom{66)999999}30\\\end{array}
Find closest multiple of 66 to 162. We see that 2 \times 66 = 132 is the nearest. Now subtract 132 from 162 to get reminder 30. Add 2 to quotient.
\text{Quotient: }1327902 \text{Reminder: }30
Since 30 is less than 66, stop the division. The reminder is 30. The topmost line 01327902 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1327902.
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}