Evaluate
72
Factor
2^{3}\times 3^{2}
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)6120}\\\end{array}
Use the 1^{st} digit 6 from dividend 6120
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)6120}\\\end{array}
Since 6 is less than 85, use the next digit 1 from dividend 6120 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)6120}\\\end{array}
Use the 2^{nd} digit 1 from dividend 6120
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)6120}\\\end{array}
Since 61 is less than 85, use the next digit 2 from dividend 6120 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)6120}\\\end{array}
Use the 3^{rd} digit 2 from dividend 6120
\begin{array}{l}\phantom{85)}007\phantom{6}\\85\overline{)6120}\\\phantom{85)}\underline{\phantom{}595\phantom{9}}\\\phantom{85)9}17\\\end{array}
Find closest multiple of 85 to 612. We see that 7 \times 85 = 595 is the nearest. Now subtract 595 from 612 to get reminder 17. Add 7 to quotient.
\begin{array}{l}\phantom{85)}007\phantom{7}\\85\overline{)6120}\\\phantom{85)}\underline{\phantom{}595\phantom{9}}\\\phantom{85)9}170\\\end{array}
Use the 4^{th} digit 0 from dividend 6120
\begin{array}{l}\phantom{85)}0072\phantom{8}\\85\overline{)6120}\\\phantom{85)}\underline{\phantom{}595\phantom{9}}\\\phantom{85)9}170\\\phantom{85)}\underline{\phantom{9}170\phantom{}}\\\phantom{85)9999}0\\\end{array}
Find closest multiple of 85 to 170. We see that 2 \times 85 = 170 is the nearest. Now subtract 170 from 170 to get reminder 0. Add 2 to quotient.
\text{Quotient: }72 \text{Reminder: }0
Since 0 is less than 85, stop the division. The reminder is 0. The topmost line 0072 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 72.
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}