Evaluate
65
Factor
5\times 13
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\begin{array}{l}\phantom{124)}\phantom{1}\\124\overline{)8060}\\\end{array}
Use the 1^{st} digit 8 from dividend 8060
\begin{array}{l}\phantom{124)}0\phantom{2}\\124\overline{)8060}\\\end{array}
Since 8 is less than 124, use the next digit 0 from dividend 8060 and add 0 to the quotient
\begin{array}{l}\phantom{124)}0\phantom{3}\\124\overline{)8060}\\\end{array}
Use the 2^{nd} digit 0 from dividend 8060
\begin{array}{l}\phantom{124)}00\phantom{4}\\124\overline{)8060}\\\end{array}
Since 80 is less than 124, use the next digit 6 from dividend 8060 and add 0 to the quotient
\begin{array}{l}\phantom{124)}00\phantom{5}\\124\overline{)8060}\\\end{array}
Use the 3^{rd} digit 6 from dividend 8060
\begin{array}{l}\phantom{124)}006\phantom{6}\\124\overline{)8060}\\\phantom{124)}\underline{\phantom{}744\phantom{9}}\\\phantom{124)9}62\\\end{array}
Find closest multiple of 124 to 806. We see that 6 \times 124 = 744 is the nearest. Now subtract 744 from 806 to get reminder 62. Add 6 to quotient.
\begin{array}{l}\phantom{124)}006\phantom{7}\\124\overline{)8060}\\\phantom{124)}\underline{\phantom{}744\phantom{9}}\\\phantom{124)9}620\\\end{array}
Use the 4^{th} digit 0 from dividend 8060
\begin{array}{l}\phantom{124)}0065\phantom{8}\\124\overline{)8060}\\\phantom{124)}\underline{\phantom{}744\phantom{9}}\\\phantom{124)9}620\\\phantom{124)}\underline{\phantom{9}620\phantom{}}\\\phantom{124)9999}0\\\end{array}
Find closest multiple of 124 to 620. We see that 5 \times 124 = 620 is the nearest. Now subtract 620 from 620 to get reminder 0. Add 5 to quotient.
\text{Quotient: }65 \text{Reminder: }0
Since 0 is less than 124, stop the division. The reminder is 0. The topmost line 0065 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 65.
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}