Evaluate
\frac{170085}{19}\approx 8951.842105263
Factor
\frac{3 \cdot 5 \cdot 17 \cdot 23 \cdot 29}{19} = 8951\frac{16}{19} = 8951.842105263158
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\begin{array}{l}\phantom{19)}\phantom{1}\\19\overline{)170085}\\\end{array}
Use the 1^{st} digit 1 from dividend 170085
\begin{array}{l}\phantom{19)}0\phantom{2}\\19\overline{)170085}\\\end{array}
Since 1 is less than 19, use the next digit 7 from dividend 170085 and add 0 to the quotient
\begin{array}{l}\phantom{19)}0\phantom{3}\\19\overline{)170085}\\\end{array}
Use the 2^{nd} digit 7 from dividend 170085
\begin{array}{l}\phantom{19)}00\phantom{4}\\19\overline{)170085}\\\end{array}
Since 17 is less than 19, use the next digit 0 from dividend 170085 and add 0 to the quotient
\begin{array}{l}\phantom{19)}00\phantom{5}\\19\overline{)170085}\\\end{array}
Use the 3^{rd} digit 0 from dividend 170085
\begin{array}{l}\phantom{19)}008\phantom{6}\\19\overline{)170085}\\\phantom{19)}\underline{\phantom{}152\phantom{999}}\\\phantom{19)9}18\\\end{array}
Find closest multiple of 19 to 170. We see that 8 \times 19 = 152 is the nearest. Now subtract 152 from 170 to get reminder 18. Add 8 to quotient.
\begin{array}{l}\phantom{19)}008\phantom{7}\\19\overline{)170085}\\\phantom{19)}\underline{\phantom{}152\phantom{999}}\\\phantom{19)9}180\\\end{array}
Use the 4^{th} digit 0 from dividend 170085
\begin{array}{l}\phantom{19)}0089\phantom{8}\\19\overline{)170085}\\\phantom{19)}\underline{\phantom{}152\phantom{999}}\\\phantom{19)9}180\\\phantom{19)}\underline{\phantom{9}171\phantom{99}}\\\phantom{19)999}9\\\end{array}
Find closest multiple of 19 to 180. We see that 9 \times 19 = 171 is the nearest. Now subtract 171 from 180 to get reminder 9. Add 9 to quotient.
\begin{array}{l}\phantom{19)}0089\phantom{9}\\19\overline{)170085}\\\phantom{19)}\underline{\phantom{}152\phantom{999}}\\\phantom{19)9}180\\\phantom{19)}\underline{\phantom{9}171\phantom{99}}\\\phantom{19)999}98\\\end{array}
Use the 5^{th} digit 8 from dividend 170085
\begin{array}{l}\phantom{19)}00895\phantom{10}\\19\overline{)170085}\\\phantom{19)}\underline{\phantom{}152\phantom{999}}\\\phantom{19)9}180\\\phantom{19)}\underline{\phantom{9}171\phantom{99}}\\\phantom{19)999}98\\\phantom{19)}\underline{\phantom{999}95\phantom{9}}\\\phantom{19)9999}3\\\end{array}
Find closest multiple of 19 to 98. We see that 5 \times 19 = 95 is the nearest. Now subtract 95 from 98 to get reminder 3. Add 5 to quotient.
\begin{array}{l}\phantom{19)}00895\phantom{11}\\19\overline{)170085}\\\phantom{19)}\underline{\phantom{}152\phantom{999}}\\\phantom{19)9}180\\\phantom{19)}\underline{\phantom{9}171\phantom{99}}\\\phantom{19)999}98\\\phantom{19)}\underline{\phantom{999}95\phantom{9}}\\\phantom{19)9999}35\\\end{array}
Use the 6^{th} digit 5 from dividend 170085
\begin{array}{l}\phantom{19)}008951\phantom{12}\\19\overline{)170085}\\\phantom{19)}\underline{\phantom{}152\phantom{999}}\\\phantom{19)9}180\\\phantom{19)}\underline{\phantom{9}171\phantom{99}}\\\phantom{19)999}98\\\phantom{19)}\underline{\phantom{999}95\phantom{9}}\\\phantom{19)9999}35\\\phantom{19)}\underline{\phantom{9999}19\phantom{}}\\\phantom{19)9999}16\\\end{array}
Find closest multiple of 19 to 35. We see that 1 \times 19 = 19 is the nearest. Now subtract 19 from 35 to get reminder 16. Add 1 to quotient.
\text{Quotient: }8951 \text{Reminder: }16
Since 16 is less than 19, stop the division. The reminder is 16. The topmost line 008951 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8951.
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}