Evaluate
965
Factor
5\times 193
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\begin{array}{l}\phantom{107)}\phantom{1}\\107\overline{)103255}\\\end{array}
Use the 1^{st} digit 1 from dividend 103255
\begin{array}{l}\phantom{107)}0\phantom{2}\\107\overline{)103255}\\\end{array}
Since 1 is less than 107, use the next digit 0 from dividend 103255 and add 0 to the quotient
\begin{array}{l}\phantom{107)}0\phantom{3}\\107\overline{)103255}\\\end{array}
Use the 2^{nd} digit 0 from dividend 103255
\begin{array}{l}\phantom{107)}00\phantom{4}\\107\overline{)103255}\\\end{array}
Since 10 is less than 107, use the next digit 3 from dividend 103255 and add 0 to the quotient
\begin{array}{l}\phantom{107)}00\phantom{5}\\107\overline{)103255}\\\end{array}
Use the 3^{rd} digit 3 from dividend 103255
\begin{array}{l}\phantom{107)}000\phantom{6}\\107\overline{)103255}\\\end{array}
Since 103 is less than 107, use the next digit 2 from dividend 103255 and add 0 to the quotient
\begin{array}{l}\phantom{107)}000\phantom{7}\\107\overline{)103255}\\\end{array}
Use the 4^{th} digit 2 from dividend 103255
\begin{array}{l}\phantom{107)}0009\phantom{8}\\107\overline{)103255}\\\phantom{107)}\underline{\phantom{9}963\phantom{99}}\\\phantom{107)99}69\\\end{array}
Find closest multiple of 107 to 1032. We see that 9 \times 107 = 963 is the nearest. Now subtract 963 from 1032 to get reminder 69. Add 9 to quotient.
\begin{array}{l}\phantom{107)}0009\phantom{9}\\107\overline{)103255}\\\phantom{107)}\underline{\phantom{9}963\phantom{99}}\\\phantom{107)99}695\\\end{array}
Use the 5^{th} digit 5 from dividend 103255
\begin{array}{l}\phantom{107)}00096\phantom{10}\\107\overline{)103255}\\\phantom{107)}\underline{\phantom{9}963\phantom{99}}\\\phantom{107)99}695\\\phantom{107)}\underline{\phantom{99}642\phantom{9}}\\\phantom{107)999}53\\\end{array}
Find closest multiple of 107 to 695. We see that 6 \times 107 = 642 is the nearest. Now subtract 642 from 695 to get reminder 53. Add 6 to quotient.
\begin{array}{l}\phantom{107)}00096\phantom{11}\\107\overline{)103255}\\\phantom{107)}\underline{\phantom{9}963\phantom{99}}\\\phantom{107)99}695\\\phantom{107)}\underline{\phantom{99}642\phantom{9}}\\\phantom{107)999}535\\\end{array}
Use the 6^{th} digit 5 from dividend 103255
\begin{array}{l}\phantom{107)}000965\phantom{12}\\107\overline{)103255}\\\phantom{107)}\underline{\phantom{9}963\phantom{99}}\\\phantom{107)99}695\\\phantom{107)}\underline{\phantom{99}642\phantom{9}}\\\phantom{107)999}535\\\phantom{107)}\underline{\phantom{999}535\phantom{}}\\\phantom{107)999999}0\\\end{array}
Find closest multiple of 107 to 535. We see that 5 \times 107 = 535 is the nearest. Now subtract 535 from 535 to get reminder 0. Add 5 to quotient.
\text{Quotient: }965 \text{Reminder: }0
Since 0 is less than 107, stop the division. The reminder is 0. The topmost line 000965 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 965.
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}