Evaluate
72
Factor
2^{3}\times 3^{2}
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\begin{array}{l}\phantom{125)}\phantom{1}\\125\overline{)9000}\\\end{array}
Use the 1^{st} digit 9 from dividend 9000
\begin{array}{l}\phantom{125)}0\phantom{2}\\125\overline{)9000}\\\end{array}
Since 9 is less than 125, use the next digit 0 from dividend 9000 and add 0 to the quotient
\begin{array}{l}\phantom{125)}0\phantom{3}\\125\overline{)9000}\\\end{array}
Use the 2^{nd} digit 0 from dividend 9000
\begin{array}{l}\phantom{125)}00\phantom{4}\\125\overline{)9000}\\\end{array}
Since 90 is less than 125, use the next digit 0 from dividend 9000 and add 0 to the quotient
\begin{array}{l}\phantom{125)}00\phantom{5}\\125\overline{)9000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 9000
\begin{array}{l}\phantom{125)}007\phantom{6}\\125\overline{)9000}\\\phantom{125)}\underline{\phantom{}875\phantom{9}}\\\phantom{125)9}25\\\end{array}
Find closest multiple of 125 to 900. We see that 7 \times 125 = 875 is the nearest. Now subtract 875 from 900 to get reminder 25. Add 7 to quotient.
\begin{array}{l}\phantom{125)}007\phantom{7}\\125\overline{)9000}\\\phantom{125)}\underline{\phantom{}875\phantom{9}}\\\phantom{125)9}250\\\end{array}
Use the 4^{th} digit 0 from dividend 9000
\begin{array}{l}\phantom{125)}0072\phantom{8}\\125\overline{)9000}\\\phantom{125)}\underline{\phantom{}875\phantom{9}}\\\phantom{125)9}250\\\phantom{125)}\underline{\phantom{9}250\phantom{}}\\\phantom{125)9999}0\\\end{array}
Find closest multiple of 125 to 250. We see that 2 \times 125 = 250 is the nearest. Now subtract 250 from 250 to get reminder 0. Add 2 to quotient.
\text{Quotient: }72 \text{Reminder: }0
Since 0 is less than 125, 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}