Evaluate
362
Factor
2\times 181
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)6516}\\\end{array}
Use the 1^{st} digit 6 from dividend 6516
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)6516}\\\end{array}
Since 6 is less than 18, use the next digit 5 from dividend 6516 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)6516}\\\end{array}
Use the 2^{nd} digit 5 from dividend 6516
\begin{array}{l}\phantom{18)}03\phantom{4}\\18\overline{)6516}\\\phantom{18)}\underline{\phantom{}54\phantom{99}}\\\phantom{18)}11\\\end{array}
Find closest multiple of 18 to 65. We see that 3 \times 18 = 54 is the nearest. Now subtract 54 from 65 to get reminder 11. Add 3 to quotient.
\begin{array}{l}\phantom{18)}03\phantom{5}\\18\overline{)6516}\\\phantom{18)}\underline{\phantom{}54\phantom{99}}\\\phantom{18)}111\\\end{array}
Use the 3^{rd} digit 1 from dividend 6516
\begin{array}{l}\phantom{18)}036\phantom{6}\\18\overline{)6516}\\\phantom{18)}\underline{\phantom{}54\phantom{99}}\\\phantom{18)}111\\\phantom{18)}\underline{\phantom{}108\phantom{9}}\\\phantom{18)99}3\\\end{array}
Find closest multiple of 18 to 111. We see that 6 \times 18 = 108 is the nearest. Now subtract 108 from 111 to get reminder 3. Add 6 to quotient.
\begin{array}{l}\phantom{18)}036\phantom{7}\\18\overline{)6516}\\\phantom{18)}\underline{\phantom{}54\phantom{99}}\\\phantom{18)}111\\\phantom{18)}\underline{\phantom{}108\phantom{9}}\\\phantom{18)99}36\\\end{array}
Use the 4^{th} digit 6 from dividend 6516
\begin{array}{l}\phantom{18)}0362\phantom{8}\\18\overline{)6516}\\\phantom{18)}\underline{\phantom{}54\phantom{99}}\\\phantom{18)}111\\\phantom{18)}\underline{\phantom{}108\phantom{9}}\\\phantom{18)99}36\\\phantom{18)}\underline{\phantom{99}36\phantom{}}\\\phantom{18)9999}0\\\end{array}
Find closest multiple of 18 to 36. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 36 to get reminder 0. Add 2 to quotient.
\text{Quotient: }362 \text{Reminder: }0
Since 0 is less than 18, stop the division. The reminder is 0. The topmost line 0362 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 362.
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}