Evaluate
205
Factor
5\times 41
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\begin{array}{l}\phantom{26)}\phantom{1}\\26\overline{)5330}\\\end{array}
Use the 1^{st} digit 5 from dividend 5330
\begin{array}{l}\phantom{26)}0\phantom{2}\\26\overline{)5330}\\\end{array}
Since 5 is less than 26, use the next digit 3 from dividend 5330 and add 0 to the quotient
\begin{array}{l}\phantom{26)}0\phantom{3}\\26\overline{)5330}\\\end{array}
Use the 2^{nd} digit 3 from dividend 5330
\begin{array}{l}\phantom{26)}02\phantom{4}\\26\overline{)5330}\\\phantom{26)}\underline{\phantom{}52\phantom{99}}\\\phantom{26)9}1\\\end{array}
Find closest multiple of 26 to 53. We see that 2 \times 26 = 52 is the nearest. Now subtract 52 from 53 to get reminder 1. Add 2 to quotient.
\begin{array}{l}\phantom{26)}02\phantom{5}\\26\overline{)5330}\\\phantom{26)}\underline{\phantom{}52\phantom{99}}\\\phantom{26)9}13\\\end{array}
Use the 3^{rd} digit 3 from dividend 5330
\begin{array}{l}\phantom{26)}020\phantom{6}\\26\overline{)5330}\\\phantom{26)}\underline{\phantom{}52\phantom{99}}\\\phantom{26)9}13\\\end{array}
Since 13 is less than 26, use the next digit 0 from dividend 5330 and add 0 to the quotient
\begin{array}{l}\phantom{26)}020\phantom{7}\\26\overline{)5330}\\\phantom{26)}\underline{\phantom{}52\phantom{99}}\\\phantom{26)9}130\\\end{array}
Use the 4^{th} digit 0 from dividend 5330
\begin{array}{l}\phantom{26)}0205\phantom{8}\\26\overline{)5330}\\\phantom{26)}\underline{\phantom{}52\phantom{99}}\\\phantom{26)9}130\\\phantom{26)}\underline{\phantom{9}130\phantom{}}\\\phantom{26)9999}0\\\end{array}
Find closest multiple of 26 to 130. We see that 5 \times 26 = 130 is the nearest. Now subtract 130 from 130 to get reminder 0. Add 5 to quotient.
\text{Quotient: }205 \text{Reminder: }0
Since 0 is less than 26, stop the division. The reminder is 0. The topmost line 0205 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 205.
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}