Evaluate
\frac{2554}{1513}\approx 1.688037013
Factor
\frac{2 \cdot 1277}{17 \cdot 89} = 1\frac{1041}{1513} = 1.6880370125578321
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\begin{array}{l}\phantom{1513)}\phantom{1}\\1513\overline{)2554}\\\end{array}
Use the 1^{st} digit 2 from dividend 2554
\begin{array}{l}\phantom{1513)}0\phantom{2}\\1513\overline{)2554}\\\end{array}
Since 2 is less than 1513, use the next digit 5 from dividend 2554 and add 0 to the quotient
\begin{array}{l}\phantom{1513)}0\phantom{3}\\1513\overline{)2554}\\\end{array}
Use the 2^{nd} digit 5 from dividend 2554
\begin{array}{l}\phantom{1513)}00\phantom{4}\\1513\overline{)2554}\\\end{array}
Since 25 is less than 1513, use the next digit 5 from dividend 2554 and add 0 to the quotient
\begin{array}{l}\phantom{1513)}00\phantom{5}\\1513\overline{)2554}\\\end{array}
Use the 3^{rd} digit 5 from dividend 2554
\begin{array}{l}\phantom{1513)}000\phantom{6}\\1513\overline{)2554}\\\end{array}
Since 255 is less than 1513, use the next digit 4 from dividend 2554 and add 0 to the quotient
\begin{array}{l}\phantom{1513)}000\phantom{7}\\1513\overline{)2554}\\\end{array}
Use the 4^{th} digit 4 from dividend 2554
\begin{array}{l}\phantom{1513)}0001\phantom{8}\\1513\overline{)2554}\\\phantom{1513)}\underline{\phantom{}1513\phantom{}}\\\phantom{1513)}1041\\\end{array}
Find closest multiple of 1513 to 2554. We see that 1 \times 1513 = 1513 is the nearest. Now subtract 1513 from 2554 to get reminder 1041. Add 1 to quotient.
\text{Quotient: }1 \text{Reminder: }1041
Since 1041 is less than 1513, stop the division. The reminder is 1041. The topmost line 0001 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
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}