Evaluate
48
Factor
2^{4}\times 3
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\begin{array}{l}\phantom{36)}\phantom{1}\\36\overline{)1728}\\\end{array}
Use the 1^{st} digit 1 from dividend 1728
\begin{array}{l}\phantom{36)}0\phantom{2}\\36\overline{)1728}\\\end{array}
Since 1 is less than 36, use the next digit 7 from dividend 1728 and add 0 to the quotient
\begin{array}{l}\phantom{36)}0\phantom{3}\\36\overline{)1728}\\\end{array}
Use the 2^{nd} digit 7 from dividend 1728
\begin{array}{l}\phantom{36)}00\phantom{4}\\36\overline{)1728}\\\end{array}
Since 17 is less than 36, use the next digit 2 from dividend 1728 and add 0 to the quotient
\begin{array}{l}\phantom{36)}00\phantom{5}\\36\overline{)1728}\\\end{array}
Use the 3^{rd} digit 2 from dividend 1728
\begin{array}{l}\phantom{36)}004\phantom{6}\\36\overline{)1728}\\\phantom{36)}\underline{\phantom{}144\phantom{9}}\\\phantom{36)9}28\\\end{array}
Find closest multiple of 36 to 172. We see that 4 \times 36 = 144 is the nearest. Now subtract 144 from 172 to get reminder 28. Add 4 to quotient.
\begin{array}{l}\phantom{36)}004\phantom{7}\\36\overline{)1728}\\\phantom{36)}\underline{\phantom{}144\phantom{9}}\\\phantom{36)9}288\\\end{array}
Use the 4^{th} digit 8 from dividend 1728
\begin{array}{l}\phantom{36)}0048\phantom{8}\\36\overline{)1728}\\\phantom{36)}\underline{\phantom{}144\phantom{9}}\\\phantom{36)9}288\\\phantom{36)}\underline{\phantom{9}288\phantom{}}\\\phantom{36)9999}0\\\end{array}
Find closest multiple of 36 to 288. We see that 8 \times 36 = 288 is the nearest. Now subtract 288 from 288 to get reminder 0. Add 8 to quotient.
\text{Quotient: }48 \text{Reminder: }0
Since 0 is less than 36, stop the division. The reminder is 0. The topmost line 0048 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 48.
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}