Evaluate
\frac{1085}{72}\approx 15.069444444
Factor
\frac{5 \cdot 7 \cdot 31}{2 ^ {3} \cdot 3 ^ {2}} = 15\frac{5}{72} = 15.069444444444445
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\begin{array}{l}\phantom{72)}\phantom{1}\\72\overline{)1085}\\\end{array}
Use the 1^{st} digit 1 from dividend 1085
\begin{array}{l}\phantom{72)}0\phantom{2}\\72\overline{)1085}\\\end{array}
Since 1 is less than 72, use the next digit 0 from dividend 1085 and add 0 to the quotient
\begin{array}{l}\phantom{72)}0\phantom{3}\\72\overline{)1085}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1085
\begin{array}{l}\phantom{72)}00\phantom{4}\\72\overline{)1085}\\\end{array}
Since 10 is less than 72, use the next digit 8 from dividend 1085 and add 0 to the quotient
\begin{array}{l}\phantom{72)}00\phantom{5}\\72\overline{)1085}\\\end{array}
Use the 3^{rd} digit 8 from dividend 1085
\begin{array}{l}\phantom{72)}001\phantom{6}\\72\overline{)1085}\\\phantom{72)}\underline{\phantom{9}72\phantom{9}}\\\phantom{72)9}36\\\end{array}
Find closest multiple of 72 to 108. We see that 1 \times 72 = 72 is the nearest. Now subtract 72 from 108 to get reminder 36. Add 1 to quotient.
\begin{array}{l}\phantom{72)}001\phantom{7}\\72\overline{)1085}\\\phantom{72)}\underline{\phantom{9}72\phantom{9}}\\\phantom{72)9}365\\\end{array}
Use the 4^{th} digit 5 from dividend 1085
\begin{array}{l}\phantom{72)}0015\phantom{8}\\72\overline{)1085}\\\phantom{72)}\underline{\phantom{9}72\phantom{9}}\\\phantom{72)9}365\\\phantom{72)}\underline{\phantom{9}360\phantom{}}\\\phantom{72)999}5\\\end{array}
Find closest multiple of 72 to 365. We see that 5 \times 72 = 360 is the nearest. Now subtract 360 from 365 to get reminder 5. Add 5 to quotient.
\text{Quotient: }15 \text{Reminder: }5
Since 5 is less than 72, stop the division. The reminder is 5. The topmost line 0015 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15.
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}