Evaluate
\frac{19062}{23}\approx 828.782608696
Factor
\frac{2 \cdot 3 ^ {3} \cdot 353}{23} = 828\frac{18}{23} = 828.7826086956521
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\begin{array}{l}\phantom{46)}\phantom{1}\\46\overline{)38124}\\\end{array}
Use the 1^{st} digit 3 from dividend 38124
\begin{array}{l}\phantom{46)}0\phantom{2}\\46\overline{)38124}\\\end{array}
Since 3 is less than 46, use the next digit 8 from dividend 38124 and add 0 to the quotient
\begin{array}{l}\phantom{46)}0\phantom{3}\\46\overline{)38124}\\\end{array}
Use the 2^{nd} digit 8 from dividend 38124
\begin{array}{l}\phantom{46)}00\phantom{4}\\46\overline{)38124}\\\end{array}
Since 38 is less than 46, use the next digit 1 from dividend 38124 and add 0 to the quotient
\begin{array}{l}\phantom{46)}00\phantom{5}\\46\overline{)38124}\\\end{array}
Use the 3^{rd} digit 1 from dividend 38124
\begin{array}{l}\phantom{46)}008\phantom{6}\\46\overline{)38124}\\\phantom{46)}\underline{\phantom{}368\phantom{99}}\\\phantom{46)9}13\\\end{array}
Find closest multiple of 46 to 381. We see that 8 \times 46 = 368 is the nearest. Now subtract 368 from 381 to get reminder 13. Add 8 to quotient.
\begin{array}{l}\phantom{46)}008\phantom{7}\\46\overline{)38124}\\\phantom{46)}\underline{\phantom{}368\phantom{99}}\\\phantom{46)9}132\\\end{array}
Use the 4^{th} digit 2 from dividend 38124
\begin{array}{l}\phantom{46)}0082\phantom{8}\\46\overline{)38124}\\\phantom{46)}\underline{\phantom{}368\phantom{99}}\\\phantom{46)9}132\\\phantom{46)}\underline{\phantom{99}92\phantom{9}}\\\phantom{46)99}40\\\end{array}
Find closest multiple of 46 to 132. We see that 2 \times 46 = 92 is the nearest. Now subtract 92 from 132 to get reminder 40. Add 2 to quotient.
\begin{array}{l}\phantom{46)}0082\phantom{9}\\46\overline{)38124}\\\phantom{46)}\underline{\phantom{}368\phantom{99}}\\\phantom{46)9}132\\\phantom{46)}\underline{\phantom{99}92\phantom{9}}\\\phantom{46)99}404\\\end{array}
Use the 5^{th} digit 4 from dividend 38124
\begin{array}{l}\phantom{46)}00828\phantom{10}\\46\overline{)38124}\\\phantom{46)}\underline{\phantom{}368\phantom{99}}\\\phantom{46)9}132\\\phantom{46)}\underline{\phantom{99}92\phantom{9}}\\\phantom{46)99}404\\\phantom{46)}\underline{\phantom{99}368\phantom{}}\\\phantom{46)999}36\\\end{array}
Find closest multiple of 46 to 404. We see that 8 \times 46 = 368 is the nearest. Now subtract 368 from 404 to get reminder 36. Add 8 to quotient.
\text{Quotient: }828 \text{Reminder: }36
Since 36 is less than 46, stop the division. The reminder is 36. The topmost line 00828 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 828.
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}