Evaluate
57
Factor
3\times 19
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\begin{array}{l}\phantom{19)}\phantom{1}\\19\overline{)1083}\\\end{array}
Use the 1^{st} digit 1 from dividend 1083
\begin{array}{l}\phantom{19)}0\phantom{2}\\19\overline{)1083}\\\end{array}
Since 1 is less than 19, use the next digit 0 from dividend 1083 and add 0 to the quotient
\begin{array}{l}\phantom{19)}0\phantom{3}\\19\overline{)1083}\\\end{array}
Use the 2^{nd} digit 0 from dividend 1083
\begin{array}{l}\phantom{19)}00\phantom{4}\\19\overline{)1083}\\\end{array}
Since 10 is less than 19, use the next digit 8 from dividend 1083 and add 0 to the quotient
\begin{array}{l}\phantom{19)}00\phantom{5}\\19\overline{)1083}\\\end{array}
Use the 3^{rd} digit 8 from dividend 1083
\begin{array}{l}\phantom{19)}005\phantom{6}\\19\overline{)1083}\\\phantom{19)}\underline{\phantom{9}95\phantom{9}}\\\phantom{19)9}13\\\end{array}
Find closest multiple of 19 to 108. We see that 5 \times 19 = 95 is the nearest. Now subtract 95 from 108 to get reminder 13. Add 5 to quotient.
\begin{array}{l}\phantom{19)}005\phantom{7}\\19\overline{)1083}\\\phantom{19)}\underline{\phantom{9}95\phantom{9}}\\\phantom{19)9}133\\\end{array}
Use the 4^{th} digit 3 from dividend 1083
\begin{array}{l}\phantom{19)}0057\phantom{8}\\19\overline{)1083}\\\phantom{19)}\underline{\phantom{9}95\phantom{9}}\\\phantom{19)9}133\\\phantom{19)}\underline{\phantom{9}133\phantom{}}\\\phantom{19)9999}0\\\end{array}
Find closest multiple of 19 to 133. We see that 7 \times 19 = 133 is the nearest. Now subtract 133 from 133 to get reminder 0. Add 7 to quotient.
\text{Quotient: }57 \text{Reminder: }0
Since 0 is less than 19, stop the division. The reminder is 0. The topmost line 0057 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 57.
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}