Evaluate
\frac{68124}{5}=13624.8
Factor
\frac{2 ^ {2} \cdot 3 \cdot 7 \cdot 811}{5} = 13624\frac{4}{5} = 13624.8
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\begin{array}{l}\phantom{50)}\phantom{1}\\50\overline{)681240}\\\end{array}
Use the 1^{st} digit 6 from dividend 681240
\begin{array}{l}\phantom{50)}0\phantom{2}\\50\overline{)681240}\\\end{array}
Since 6 is less than 50, use the next digit 8 from dividend 681240 and add 0 to the quotient
\begin{array}{l}\phantom{50)}0\phantom{3}\\50\overline{)681240}\\\end{array}
Use the 2^{nd} digit 8 from dividend 681240
\begin{array}{l}\phantom{50)}01\phantom{4}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}18\\\end{array}
Find closest multiple of 50 to 68. We see that 1 \times 50 = 50 is the nearest. Now subtract 50 from 68 to get reminder 18. Add 1 to quotient.
\begin{array}{l}\phantom{50)}01\phantom{5}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}181\\\end{array}
Use the 3^{rd} digit 1 from dividend 681240
\begin{array}{l}\phantom{50)}013\phantom{6}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}181\\\phantom{50)}\underline{\phantom{}150\phantom{999}}\\\phantom{50)9}31\\\end{array}
Find closest multiple of 50 to 181. We see that 3 \times 50 = 150 is the nearest. Now subtract 150 from 181 to get reminder 31. Add 3 to quotient.
\begin{array}{l}\phantom{50)}013\phantom{7}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}181\\\phantom{50)}\underline{\phantom{}150\phantom{999}}\\\phantom{50)9}312\\\end{array}
Use the 4^{th} digit 2 from dividend 681240
\begin{array}{l}\phantom{50)}0136\phantom{8}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}181\\\phantom{50)}\underline{\phantom{}150\phantom{999}}\\\phantom{50)9}312\\\phantom{50)}\underline{\phantom{9}300\phantom{99}}\\\phantom{50)99}12\\\end{array}
Find closest multiple of 50 to 312. We see that 6 \times 50 = 300 is the nearest. Now subtract 300 from 312 to get reminder 12. Add 6 to quotient.
\begin{array}{l}\phantom{50)}0136\phantom{9}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}181\\\phantom{50)}\underline{\phantom{}150\phantom{999}}\\\phantom{50)9}312\\\phantom{50)}\underline{\phantom{9}300\phantom{99}}\\\phantom{50)99}124\\\end{array}
Use the 5^{th} digit 4 from dividend 681240
\begin{array}{l}\phantom{50)}01362\phantom{10}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}181\\\phantom{50)}\underline{\phantom{}150\phantom{999}}\\\phantom{50)9}312\\\phantom{50)}\underline{\phantom{9}300\phantom{99}}\\\phantom{50)99}124\\\phantom{50)}\underline{\phantom{99}100\phantom{9}}\\\phantom{50)999}24\\\end{array}
Find closest multiple of 50 to 124. We see that 2 \times 50 = 100 is the nearest. Now subtract 100 from 124 to get reminder 24. Add 2 to quotient.
\begin{array}{l}\phantom{50)}01362\phantom{11}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}181\\\phantom{50)}\underline{\phantom{}150\phantom{999}}\\\phantom{50)9}312\\\phantom{50)}\underline{\phantom{9}300\phantom{99}}\\\phantom{50)99}124\\\phantom{50)}\underline{\phantom{99}100\phantom{9}}\\\phantom{50)999}240\\\end{array}
Use the 6^{th} digit 0 from dividend 681240
\begin{array}{l}\phantom{50)}013624\phantom{12}\\50\overline{)681240}\\\phantom{50)}\underline{\phantom{}50\phantom{9999}}\\\phantom{50)}181\\\phantom{50)}\underline{\phantom{}150\phantom{999}}\\\phantom{50)9}312\\\phantom{50)}\underline{\phantom{9}300\phantom{99}}\\\phantom{50)99}124\\\phantom{50)}\underline{\phantom{99}100\phantom{9}}\\\phantom{50)999}240\\\phantom{50)}\underline{\phantom{999}200\phantom{}}\\\phantom{50)9999}40\\\end{array}
Find closest multiple of 50 to 240. We see that 4 \times 50 = 200 is the nearest. Now subtract 200 from 240 to get reminder 40. Add 4 to quotient.
\text{Quotient: }13624 \text{Reminder: }40
Since 40 is less than 50, stop the division. The reminder is 40. The topmost line 013624 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13624.
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}