Evaluate
\frac{2413}{13}\approx 185.615384615
Factor
\frac{19 \cdot 127}{13} = 185\frac{8}{13} = 185.6153846153846
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)2413}\\\end{array}
Use the 1^{st} digit 2 from dividend 2413
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)2413}\\\end{array}
Since 2 is less than 13, use the next digit 4 from dividend 2413 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)2413}\\\end{array}
Use the 2^{nd} digit 4 from dividend 2413
\begin{array}{l}\phantom{13)}01\phantom{4}\\13\overline{)2413}\\\phantom{13)}\underline{\phantom{}13\phantom{99}}\\\phantom{13)}11\\\end{array}
Find closest multiple of 13 to 24. We see that 1 \times 13 = 13 is the nearest. Now subtract 13 from 24 to get reminder 11. Add 1 to quotient.
\begin{array}{l}\phantom{13)}01\phantom{5}\\13\overline{)2413}\\\phantom{13)}\underline{\phantom{}13\phantom{99}}\\\phantom{13)}111\\\end{array}
Use the 3^{rd} digit 1 from dividend 2413
\begin{array}{l}\phantom{13)}018\phantom{6}\\13\overline{)2413}\\\phantom{13)}\underline{\phantom{}13\phantom{99}}\\\phantom{13)}111\\\phantom{13)}\underline{\phantom{}104\phantom{9}}\\\phantom{13)99}7\\\end{array}
Find closest multiple of 13 to 111. We see that 8 \times 13 = 104 is the nearest. Now subtract 104 from 111 to get reminder 7. Add 8 to quotient.
\begin{array}{l}\phantom{13)}018\phantom{7}\\13\overline{)2413}\\\phantom{13)}\underline{\phantom{}13\phantom{99}}\\\phantom{13)}111\\\phantom{13)}\underline{\phantom{}104\phantom{9}}\\\phantom{13)99}73\\\end{array}
Use the 4^{th} digit 3 from dividend 2413
\begin{array}{l}\phantom{13)}0185\phantom{8}\\13\overline{)2413}\\\phantom{13)}\underline{\phantom{}13\phantom{99}}\\\phantom{13)}111\\\phantom{13)}\underline{\phantom{}104\phantom{9}}\\\phantom{13)99}73\\\phantom{13)}\underline{\phantom{99}65\phantom{}}\\\phantom{13)999}8\\\end{array}
Find closest multiple of 13 to 73. We see that 5 \times 13 = 65 is the nearest. Now subtract 65 from 73 to get reminder 8. Add 5 to quotient.
\text{Quotient: }185 \text{Reminder: }8
Since 8 is less than 13, stop the division. The reminder is 8. The topmost line 0185 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 185.
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}