Evaluate
\frac{66497}{18}\approx 3694.277777778
Factor
\frac{29 \cdot 2293}{2 \cdot 3 ^ {2}} = 3694\frac{5}{18} = 3694.277777777778
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)66497}\\\end{array}
Use the 1^{st} digit 6 from dividend 66497
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)66497}\\\end{array}
Since 6 is less than 18, use the next digit 6 from dividend 66497 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)66497}\\\end{array}
Use the 2^{nd} digit 6 from dividend 66497
\begin{array}{l}\phantom{18)}03\phantom{4}\\18\overline{)66497}\\\phantom{18)}\underline{\phantom{}54\phantom{999}}\\\phantom{18)}12\\\end{array}
Find closest multiple of 18 to 66. We see that 3 \times 18 = 54 is the nearest. Now subtract 54 from 66 to get reminder 12. Add 3 to quotient.
\begin{array}{l}\phantom{18)}03\phantom{5}\\18\overline{)66497}\\\phantom{18)}\underline{\phantom{}54\phantom{999}}\\\phantom{18)}124\\\end{array}
Use the 3^{rd} digit 4 from dividend 66497
\begin{array}{l}\phantom{18)}036\phantom{6}\\18\overline{)66497}\\\phantom{18)}\underline{\phantom{}54\phantom{999}}\\\phantom{18)}124\\\phantom{18)}\underline{\phantom{}108\phantom{99}}\\\phantom{18)9}16\\\end{array}
Find closest multiple of 18 to 124. We see that 6 \times 18 = 108 is the nearest. Now subtract 108 from 124 to get reminder 16. Add 6 to quotient.
\begin{array}{l}\phantom{18)}036\phantom{7}\\18\overline{)66497}\\\phantom{18)}\underline{\phantom{}54\phantom{999}}\\\phantom{18)}124\\\phantom{18)}\underline{\phantom{}108\phantom{99}}\\\phantom{18)9}169\\\end{array}
Use the 4^{th} digit 9 from dividend 66497
\begin{array}{l}\phantom{18)}0369\phantom{8}\\18\overline{)66497}\\\phantom{18)}\underline{\phantom{}54\phantom{999}}\\\phantom{18)}124\\\phantom{18)}\underline{\phantom{}108\phantom{99}}\\\phantom{18)9}169\\\phantom{18)}\underline{\phantom{9}162\phantom{9}}\\\phantom{18)999}7\\\end{array}
Find closest multiple of 18 to 169. We see that 9 \times 18 = 162 is the nearest. Now subtract 162 from 169 to get reminder 7. Add 9 to quotient.
\begin{array}{l}\phantom{18)}0369\phantom{9}\\18\overline{)66497}\\\phantom{18)}\underline{\phantom{}54\phantom{999}}\\\phantom{18)}124\\\phantom{18)}\underline{\phantom{}108\phantom{99}}\\\phantom{18)9}169\\\phantom{18)}\underline{\phantom{9}162\phantom{9}}\\\phantom{18)999}77\\\end{array}
Use the 5^{th} digit 7 from dividend 66497
\begin{array}{l}\phantom{18)}03694\phantom{10}\\18\overline{)66497}\\\phantom{18)}\underline{\phantom{}54\phantom{999}}\\\phantom{18)}124\\\phantom{18)}\underline{\phantom{}108\phantom{99}}\\\phantom{18)9}169\\\phantom{18)}\underline{\phantom{9}162\phantom{9}}\\\phantom{18)999}77\\\phantom{18)}\underline{\phantom{999}72\phantom{}}\\\phantom{18)9999}5\\\end{array}
Find closest multiple of 18 to 77. We see that 4 \times 18 = 72 is the nearest. Now subtract 72 from 77 to get reminder 5. Add 4 to quotient.
\text{Quotient: }3694 \text{Reminder: }5
Since 5 is less than 18, stop the division. The reminder is 5. The topmost line 03694 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3694.
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}