Evaluate
\frac{42434}{5}=8486.8
Factor
\frac{2 \cdot 7 ^ {2} \cdot 433}{5} = 8486\frac{4}{5} = 8486.8
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)721378}\\\end{array}
Use the 1^{st} digit 7 from dividend 721378
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)721378}\\\end{array}
Since 7 is less than 85, use the next digit 2 from dividend 721378 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)721378}\\\end{array}
Use the 2^{nd} digit 2 from dividend 721378
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)721378}\\\end{array}
Since 72 is less than 85, use the next digit 1 from dividend 721378 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)721378}\\\end{array}
Use the 3^{rd} digit 1 from dividend 721378
\begin{array}{l}\phantom{85)}008\phantom{6}\\85\overline{)721378}\\\phantom{85)}\underline{\phantom{}680\phantom{999}}\\\phantom{85)9}41\\\end{array}
Find closest multiple of 85 to 721. We see that 8 \times 85 = 680 is the nearest. Now subtract 680 from 721 to get reminder 41. Add 8 to quotient.
\begin{array}{l}\phantom{85)}008\phantom{7}\\85\overline{)721378}\\\phantom{85)}\underline{\phantom{}680\phantom{999}}\\\phantom{85)9}413\\\end{array}
Use the 4^{th} digit 3 from dividend 721378
\begin{array}{l}\phantom{85)}0084\phantom{8}\\85\overline{)721378}\\\phantom{85)}\underline{\phantom{}680\phantom{999}}\\\phantom{85)9}413\\\phantom{85)}\underline{\phantom{9}340\phantom{99}}\\\phantom{85)99}73\\\end{array}
Find closest multiple of 85 to 413. We see that 4 \times 85 = 340 is the nearest. Now subtract 340 from 413 to get reminder 73. Add 4 to quotient.
\begin{array}{l}\phantom{85)}0084\phantom{9}\\85\overline{)721378}\\\phantom{85)}\underline{\phantom{}680\phantom{999}}\\\phantom{85)9}413\\\phantom{85)}\underline{\phantom{9}340\phantom{99}}\\\phantom{85)99}737\\\end{array}
Use the 5^{th} digit 7 from dividend 721378
\begin{array}{l}\phantom{85)}00848\phantom{10}\\85\overline{)721378}\\\phantom{85)}\underline{\phantom{}680\phantom{999}}\\\phantom{85)9}413\\\phantom{85)}\underline{\phantom{9}340\phantom{99}}\\\phantom{85)99}737\\\phantom{85)}\underline{\phantom{99}680\phantom{9}}\\\phantom{85)999}57\\\end{array}
Find closest multiple of 85 to 737. We see that 8 \times 85 = 680 is the nearest. Now subtract 680 from 737 to get reminder 57. Add 8 to quotient.
\begin{array}{l}\phantom{85)}00848\phantom{11}\\85\overline{)721378}\\\phantom{85)}\underline{\phantom{}680\phantom{999}}\\\phantom{85)9}413\\\phantom{85)}\underline{\phantom{9}340\phantom{99}}\\\phantom{85)99}737\\\phantom{85)}\underline{\phantom{99}680\phantom{9}}\\\phantom{85)999}578\\\end{array}
Use the 6^{th} digit 8 from dividend 721378
\begin{array}{l}\phantom{85)}008486\phantom{12}\\85\overline{)721378}\\\phantom{85)}\underline{\phantom{}680\phantom{999}}\\\phantom{85)9}413\\\phantom{85)}\underline{\phantom{9}340\phantom{99}}\\\phantom{85)99}737\\\phantom{85)}\underline{\phantom{99}680\phantom{9}}\\\phantom{85)999}578\\\phantom{85)}\underline{\phantom{999}510\phantom{}}\\\phantom{85)9999}68\\\end{array}
Find closest multiple of 85 to 578. We see that 6 \times 85 = 510 is the nearest. Now subtract 510 from 578 to get reminder 68. Add 6 to quotient.
\text{Quotient: }8486 \text{Reminder: }68
Since 68 is less than 85, stop the division. The reminder is 68. The topmost line 008486 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8486.
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}