Evaluate
305
Factor
5\times 61
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\begin{array}{l}\phantom{76)}\phantom{1}\\76\overline{)23180}\\\end{array}
Use the 1^{st} digit 2 from dividend 23180
\begin{array}{l}\phantom{76)}0\phantom{2}\\76\overline{)23180}\\\end{array}
Since 2 is less than 76, use the next digit 3 from dividend 23180 and add 0 to the quotient
\begin{array}{l}\phantom{76)}0\phantom{3}\\76\overline{)23180}\\\end{array}
Use the 2^{nd} digit 3 from dividend 23180
\begin{array}{l}\phantom{76)}00\phantom{4}\\76\overline{)23180}\\\end{array}
Since 23 is less than 76, use the next digit 1 from dividend 23180 and add 0 to the quotient
\begin{array}{l}\phantom{76)}00\phantom{5}\\76\overline{)23180}\\\end{array}
Use the 3^{rd} digit 1 from dividend 23180
\begin{array}{l}\phantom{76)}003\phantom{6}\\76\overline{)23180}\\\phantom{76)}\underline{\phantom{}228\phantom{99}}\\\phantom{76)99}3\\\end{array}
Find closest multiple of 76 to 231. We see that 3 \times 76 = 228 is the nearest. Now subtract 228 from 231 to get reminder 3. Add 3 to quotient.
\begin{array}{l}\phantom{76)}003\phantom{7}\\76\overline{)23180}\\\phantom{76)}\underline{\phantom{}228\phantom{99}}\\\phantom{76)99}38\\\end{array}
Use the 4^{th} digit 8 from dividend 23180
\begin{array}{l}\phantom{76)}0030\phantom{8}\\76\overline{)23180}\\\phantom{76)}\underline{\phantom{}228\phantom{99}}\\\phantom{76)99}38\\\end{array}
Since 38 is less than 76, use the next digit 0 from dividend 23180 and add 0 to the quotient
\begin{array}{l}\phantom{76)}0030\phantom{9}\\76\overline{)23180}\\\phantom{76)}\underline{\phantom{}228\phantom{99}}\\\phantom{76)99}380\\\end{array}
Use the 5^{th} digit 0 from dividend 23180
\begin{array}{l}\phantom{76)}00305\phantom{10}\\76\overline{)23180}\\\phantom{76)}\underline{\phantom{}228\phantom{99}}\\\phantom{76)99}380\\\phantom{76)}\underline{\phantom{99}380\phantom{}}\\\phantom{76)99999}0\\\end{array}
Find closest multiple of 76 to 380. We see that 5 \times 76 = 380 is the nearest. Now subtract 380 from 380 to get reminder 0. Add 5 to quotient.
\text{Quotient: }305 \text{Reminder: }0
Since 0 is less than 76, stop the division. The reminder is 0. The topmost line 00305 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 305.
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}