Evaluate
\frac{15625}{729}\approx 21.433470508
Factor
\frac{5 ^ {6}}{3 ^ {6}} = 21\frac{316}{729} = 21.43347050754458
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\begin{array}{l}\phantom{729)}\phantom{1}\\729\overline{)15625}\\\end{array}
Use the 1^{st} digit 1 from dividend 15625
\begin{array}{l}\phantom{729)}0\phantom{2}\\729\overline{)15625}\\\end{array}
Since 1 is less than 729, use the next digit 5 from dividend 15625 and add 0 to the quotient
\begin{array}{l}\phantom{729)}0\phantom{3}\\729\overline{)15625}\\\end{array}
Use the 2^{nd} digit 5 from dividend 15625
\begin{array}{l}\phantom{729)}00\phantom{4}\\729\overline{)15625}\\\end{array}
Since 15 is less than 729, use the next digit 6 from dividend 15625 and add 0 to the quotient
\begin{array}{l}\phantom{729)}00\phantom{5}\\729\overline{)15625}\\\end{array}
Use the 3^{rd} digit 6 from dividend 15625
\begin{array}{l}\phantom{729)}000\phantom{6}\\729\overline{)15625}\\\end{array}
Since 156 is less than 729, use the next digit 2 from dividend 15625 and add 0 to the quotient
\begin{array}{l}\phantom{729)}000\phantom{7}\\729\overline{)15625}\\\end{array}
Use the 4^{th} digit 2 from dividend 15625
\begin{array}{l}\phantom{729)}0002\phantom{8}\\729\overline{)15625}\\\phantom{729)}\underline{\phantom{}1458\phantom{9}}\\\phantom{729)9}104\\\end{array}
Find closest multiple of 729 to 1562. We see that 2 \times 729 = 1458 is the nearest. Now subtract 1458 from 1562 to get reminder 104. Add 2 to quotient.
\begin{array}{l}\phantom{729)}0002\phantom{9}\\729\overline{)15625}\\\phantom{729)}\underline{\phantom{}1458\phantom{9}}\\\phantom{729)9}1045\\\end{array}
Use the 5^{th} digit 5 from dividend 15625
\begin{array}{l}\phantom{729)}00021\phantom{10}\\729\overline{)15625}\\\phantom{729)}\underline{\phantom{}1458\phantom{9}}\\\phantom{729)9}1045\\\phantom{729)}\underline{\phantom{99}729\phantom{}}\\\phantom{729)99}316\\\end{array}
Find closest multiple of 729 to 1045. We see that 1 \times 729 = 729 is the nearest. Now subtract 729 from 1045 to get reminder 316. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }316
Since 316 is less than 729, stop the division. The reminder is 316. The topmost line 00021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
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}