Evaluate
108
Factor
2^{2}\times 3^{3}
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)7020}\\\end{array}
Use the 1^{st} digit 7 from dividend 7020
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)7020}\\\end{array}
Since 7 is less than 65, use the next digit 0 from dividend 7020 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)7020}\\\end{array}
Use the 2^{nd} digit 0 from dividend 7020
\begin{array}{l}\phantom{65)}01\phantom{4}\\65\overline{)7020}\\\phantom{65)}\underline{\phantom{}65\phantom{99}}\\\phantom{65)9}5\\\end{array}
Find closest multiple of 65 to 70. We see that 1 \times 65 = 65 is the nearest. Now subtract 65 from 70 to get reminder 5. Add 1 to quotient.
\begin{array}{l}\phantom{65)}01\phantom{5}\\65\overline{)7020}\\\phantom{65)}\underline{\phantom{}65\phantom{99}}\\\phantom{65)9}52\\\end{array}
Use the 3^{rd} digit 2 from dividend 7020
\begin{array}{l}\phantom{65)}010\phantom{6}\\65\overline{)7020}\\\phantom{65)}\underline{\phantom{}65\phantom{99}}\\\phantom{65)9}52\\\end{array}
Since 52 is less than 65, use the next digit 0 from dividend 7020 and add 0 to the quotient
\begin{array}{l}\phantom{65)}010\phantom{7}\\65\overline{)7020}\\\phantom{65)}\underline{\phantom{}65\phantom{99}}\\\phantom{65)9}520\\\end{array}
Use the 4^{th} digit 0 from dividend 7020
\begin{array}{l}\phantom{65)}0108\phantom{8}\\65\overline{)7020}\\\phantom{65)}\underline{\phantom{}65\phantom{99}}\\\phantom{65)9}520\\\phantom{65)}\underline{\phantom{9}520\phantom{}}\\\phantom{65)9999}0\\\end{array}
Find closest multiple of 65 to 520. We see that 8 \times 65 = 520 is the nearest. Now subtract 520 from 520 to get reminder 0. Add 8 to quotient.
\text{Quotient: }108 \text{Reminder: }0
Since 0 is less than 65, stop the division. The reminder is 0. The topmost line 0108 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 108.
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}