Evaluate
86
Factor
2\times 43
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\begin{array}{l}\phantom{78)}\phantom{1}\\78\overline{)6708}\\\end{array}
Use the 1^{st} digit 6 from dividend 6708
\begin{array}{l}\phantom{78)}0\phantom{2}\\78\overline{)6708}\\\end{array}
Since 6 is less than 78, use the next digit 7 from dividend 6708 and add 0 to the quotient
\begin{array}{l}\phantom{78)}0\phantom{3}\\78\overline{)6708}\\\end{array}
Use the 2^{nd} digit 7 from dividend 6708
\begin{array}{l}\phantom{78)}00\phantom{4}\\78\overline{)6708}\\\end{array}
Since 67 is less than 78, use the next digit 0 from dividend 6708 and add 0 to the quotient
\begin{array}{l}\phantom{78)}00\phantom{5}\\78\overline{)6708}\\\end{array}
Use the 3^{rd} digit 0 from dividend 6708
\begin{array}{l}\phantom{78)}008\phantom{6}\\78\overline{)6708}\\\phantom{78)}\underline{\phantom{}624\phantom{9}}\\\phantom{78)9}46\\\end{array}
Find closest multiple of 78 to 670. We see that 8 \times 78 = 624 is the nearest. Now subtract 624 from 670 to get reminder 46. Add 8 to quotient.
\begin{array}{l}\phantom{78)}008\phantom{7}\\78\overline{)6708}\\\phantom{78)}\underline{\phantom{}624\phantom{9}}\\\phantom{78)9}468\\\end{array}
Use the 4^{th} digit 8 from dividend 6708
\begin{array}{l}\phantom{78)}0086\phantom{8}\\78\overline{)6708}\\\phantom{78)}\underline{\phantom{}624\phantom{9}}\\\phantom{78)9}468\\\phantom{78)}\underline{\phantom{9}468\phantom{}}\\\phantom{78)9999}0\\\end{array}
Find closest multiple of 78 to 468. We see that 6 \times 78 = 468 is the nearest. Now subtract 468 from 468 to get reminder 0. Add 6 to quotient.
\text{Quotient: }86 \text{Reminder: }0
Since 0 is less than 78, stop the division. The reminder is 0. The topmost line 0086 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 86.
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}