Evaluate
1706
Factor
2\times 853
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\begin{array}{l}\phantom{40)}\phantom{1}\\40\overline{)68240}\\\end{array}
Use the 1^{st} digit 6 from dividend 68240
\begin{array}{l}\phantom{40)}0\phantom{2}\\40\overline{)68240}\\\end{array}
Since 6 is less than 40, use the next digit 8 from dividend 68240 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0\phantom{3}\\40\overline{)68240}\\\end{array}
Use the 2^{nd} digit 8 from dividend 68240
\begin{array}{l}\phantom{40)}01\phantom{4}\\40\overline{)68240}\\\phantom{40)}\underline{\phantom{}40\phantom{999}}\\\phantom{40)}28\\\end{array}
Find closest multiple of 40 to 68. We see that 1 \times 40 = 40 is the nearest. Now subtract 40 from 68 to get reminder 28. Add 1 to quotient.
\begin{array}{l}\phantom{40)}01\phantom{5}\\40\overline{)68240}\\\phantom{40)}\underline{\phantom{}40\phantom{999}}\\\phantom{40)}282\\\end{array}
Use the 3^{rd} digit 2 from dividend 68240
\begin{array}{l}\phantom{40)}017\phantom{6}\\40\overline{)68240}\\\phantom{40)}\underline{\phantom{}40\phantom{999}}\\\phantom{40)}282\\\phantom{40)}\underline{\phantom{}280\phantom{99}}\\\phantom{40)99}2\\\end{array}
Find closest multiple of 40 to 282. We see that 7 \times 40 = 280 is the nearest. Now subtract 280 from 282 to get reminder 2. Add 7 to quotient.
\begin{array}{l}\phantom{40)}017\phantom{7}\\40\overline{)68240}\\\phantom{40)}\underline{\phantom{}40\phantom{999}}\\\phantom{40)}282\\\phantom{40)}\underline{\phantom{}280\phantom{99}}\\\phantom{40)99}24\\\end{array}
Use the 4^{th} digit 4 from dividend 68240
\begin{array}{l}\phantom{40)}0170\phantom{8}\\40\overline{)68240}\\\phantom{40)}\underline{\phantom{}40\phantom{999}}\\\phantom{40)}282\\\phantom{40)}\underline{\phantom{}280\phantom{99}}\\\phantom{40)99}24\\\end{array}
Since 24 is less than 40, use the next digit 0 from dividend 68240 and add 0 to the quotient
\begin{array}{l}\phantom{40)}0170\phantom{9}\\40\overline{)68240}\\\phantom{40)}\underline{\phantom{}40\phantom{999}}\\\phantom{40)}282\\\phantom{40)}\underline{\phantom{}280\phantom{99}}\\\phantom{40)99}240\\\end{array}
Use the 5^{th} digit 0 from dividend 68240
\begin{array}{l}\phantom{40)}01706\phantom{10}\\40\overline{)68240}\\\phantom{40)}\underline{\phantom{}40\phantom{999}}\\\phantom{40)}282\\\phantom{40)}\underline{\phantom{}280\phantom{99}}\\\phantom{40)99}240\\\phantom{40)}\underline{\phantom{99}240\phantom{}}\\\phantom{40)99999}0\\\end{array}
Find closest multiple of 40 to 240. We see that 6 \times 40 = 240 is the nearest. Now subtract 240 from 240 to get reminder 0. Add 6 to quotient.
\text{Quotient: }1706 \text{Reminder: }0
Since 0 is less than 40, stop the division. The reminder is 0. The topmost line 01706 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1706.
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}