Evaluate
\frac{11466}{107}\approx 107.158878505
Factor
\frac{2 \cdot 3 ^ {2} \cdot 7 ^ {2} \cdot 13}{107} = 107\frac{17}{107} = 107.1588785046729
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\begin{array}{l}\phantom{428)}\phantom{1}\\428\overline{)45864}\\\end{array}
Use the 1^{st} digit 4 from dividend 45864
\begin{array}{l}\phantom{428)}0\phantom{2}\\428\overline{)45864}\\\end{array}
Since 4 is less than 428, use the next digit 5 from dividend 45864 and add 0 to the quotient
\begin{array}{l}\phantom{428)}0\phantom{3}\\428\overline{)45864}\\\end{array}
Use the 2^{nd} digit 5 from dividend 45864
\begin{array}{l}\phantom{428)}00\phantom{4}\\428\overline{)45864}\\\end{array}
Since 45 is less than 428, use the next digit 8 from dividend 45864 and add 0 to the quotient
\begin{array}{l}\phantom{428)}00\phantom{5}\\428\overline{)45864}\\\end{array}
Use the 3^{rd} digit 8 from dividend 45864
\begin{array}{l}\phantom{428)}001\phantom{6}\\428\overline{)45864}\\\phantom{428)}\underline{\phantom{}428\phantom{99}}\\\phantom{428)9}30\\\end{array}
Find closest multiple of 428 to 458. We see that 1 \times 428 = 428 is the nearest. Now subtract 428 from 458 to get reminder 30. Add 1 to quotient.
\begin{array}{l}\phantom{428)}001\phantom{7}\\428\overline{)45864}\\\phantom{428)}\underline{\phantom{}428\phantom{99}}\\\phantom{428)9}306\\\end{array}
Use the 4^{th} digit 6 from dividend 45864
\begin{array}{l}\phantom{428)}0010\phantom{8}\\428\overline{)45864}\\\phantom{428)}\underline{\phantom{}428\phantom{99}}\\\phantom{428)9}306\\\end{array}
Since 306 is less than 428, use the next digit 4 from dividend 45864 and add 0 to the quotient
\begin{array}{l}\phantom{428)}0010\phantom{9}\\428\overline{)45864}\\\phantom{428)}\underline{\phantom{}428\phantom{99}}\\\phantom{428)9}3064\\\end{array}
Use the 5^{th} digit 4 from dividend 45864
\begin{array}{l}\phantom{428)}00107\phantom{10}\\428\overline{)45864}\\\phantom{428)}\underline{\phantom{}428\phantom{99}}\\\phantom{428)9}3064\\\phantom{428)}\underline{\phantom{9}2996\phantom{}}\\\phantom{428)999}68\\\end{array}
Find closest multiple of 428 to 3064. We see that 7 \times 428 = 2996 is the nearest. Now subtract 2996 from 3064 to get reminder 68. Add 7 to quotient.
\text{Quotient: }107 \text{Reminder: }68
Since 68 is less than 428, stop the division. The reminder is 68. The topmost line 00107 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 107.
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}