Evaluate
\frac{58308}{155}\approx 376.180645161
Factor
\frac{2 ^ {2} \cdot 3 \cdot 43 \cdot 113}{5 \cdot 31} = 376\frac{28}{155} = 376.18064516129033
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\begin{array}{l}\phantom{2015)}\phantom{1}\\2015\overline{)758004}\\\end{array}
Use the 1^{st} digit 7 from dividend 758004
\begin{array}{l}\phantom{2015)}0\phantom{2}\\2015\overline{)758004}\\\end{array}
Since 7 is less than 2015, use the next digit 5 from dividend 758004 and add 0 to the quotient
\begin{array}{l}\phantom{2015)}0\phantom{3}\\2015\overline{)758004}\\\end{array}
Use the 2^{nd} digit 5 from dividend 758004
\begin{array}{l}\phantom{2015)}00\phantom{4}\\2015\overline{)758004}\\\end{array}
Since 75 is less than 2015, use the next digit 8 from dividend 758004 and add 0 to the quotient
\begin{array}{l}\phantom{2015)}00\phantom{5}\\2015\overline{)758004}\\\end{array}
Use the 3^{rd} digit 8 from dividend 758004
\begin{array}{l}\phantom{2015)}000\phantom{6}\\2015\overline{)758004}\\\end{array}
Since 758 is less than 2015, use the next digit 0 from dividend 758004 and add 0 to the quotient
\begin{array}{l}\phantom{2015)}000\phantom{7}\\2015\overline{)758004}\\\end{array}
Use the 4^{th} digit 0 from dividend 758004
\begin{array}{l}\phantom{2015)}0003\phantom{8}\\2015\overline{)758004}\\\phantom{2015)}\underline{\phantom{}6045\phantom{99}}\\\phantom{2015)}1535\\\end{array}
Find closest multiple of 2015 to 7580. We see that 3 \times 2015 = 6045 is the nearest. Now subtract 6045 from 7580 to get reminder 1535. Add 3 to quotient.
\begin{array}{l}\phantom{2015)}0003\phantom{9}\\2015\overline{)758004}\\\phantom{2015)}\underline{\phantom{}6045\phantom{99}}\\\phantom{2015)}15350\\\end{array}
Use the 5^{th} digit 0 from dividend 758004
\begin{array}{l}\phantom{2015)}00037\phantom{10}\\2015\overline{)758004}\\\phantom{2015)}\underline{\phantom{}6045\phantom{99}}\\\phantom{2015)}15350\\\phantom{2015)}\underline{\phantom{}14105\phantom{9}}\\\phantom{2015)9}1245\\\end{array}
Find closest multiple of 2015 to 15350. We see that 7 \times 2015 = 14105 is the nearest. Now subtract 14105 from 15350 to get reminder 1245. Add 7 to quotient.
\begin{array}{l}\phantom{2015)}00037\phantom{11}\\2015\overline{)758004}\\\phantom{2015)}\underline{\phantom{}6045\phantom{99}}\\\phantom{2015)}15350\\\phantom{2015)}\underline{\phantom{}14105\phantom{9}}\\\phantom{2015)9}12454\\\end{array}
Use the 6^{th} digit 4 from dividend 758004
\begin{array}{l}\phantom{2015)}000376\phantom{12}\\2015\overline{)758004}\\\phantom{2015)}\underline{\phantom{}6045\phantom{99}}\\\phantom{2015)}15350\\\phantom{2015)}\underline{\phantom{}14105\phantom{9}}\\\phantom{2015)9}12454\\\phantom{2015)}\underline{\phantom{9}12090\phantom{}}\\\phantom{2015)999}364\\\end{array}
Find closest multiple of 2015 to 12454. We see that 6 \times 2015 = 12090 is the nearest. Now subtract 12090 from 12454 to get reminder 364. Add 6 to quotient.
\text{Quotient: }376 \text{Reminder: }364
Since 364 is less than 2015, stop the division. The reminder is 364. The topmost line 000376 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 376.
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}