Evaluate
65
Factor
5\times 13
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\begin{array}{l}\phantom{98)}\phantom{1}\\98\overline{)6370}\\\end{array}
Use the 1^{st} digit 6 from dividend 6370
\begin{array}{l}\phantom{98)}0\phantom{2}\\98\overline{)6370}\\\end{array}
Since 6 is less than 98, use the next digit 3 from dividend 6370 and add 0 to the quotient
\begin{array}{l}\phantom{98)}0\phantom{3}\\98\overline{)6370}\\\end{array}
Use the 2^{nd} digit 3 from dividend 6370
\begin{array}{l}\phantom{98)}00\phantom{4}\\98\overline{)6370}\\\end{array}
Since 63 is less than 98, use the next digit 7 from dividend 6370 and add 0 to the quotient
\begin{array}{l}\phantom{98)}00\phantom{5}\\98\overline{)6370}\\\end{array}
Use the 3^{rd} digit 7 from dividend 6370
\begin{array}{l}\phantom{98)}006\phantom{6}\\98\overline{)6370}\\\phantom{98)}\underline{\phantom{}588\phantom{9}}\\\phantom{98)9}49\\\end{array}
Find closest multiple of 98 to 637. We see that 6 \times 98 = 588 is the nearest. Now subtract 588 from 637 to get reminder 49. Add 6 to quotient.
\begin{array}{l}\phantom{98)}006\phantom{7}\\98\overline{)6370}\\\phantom{98)}\underline{\phantom{}588\phantom{9}}\\\phantom{98)9}490\\\end{array}
Use the 4^{th} digit 0 from dividend 6370
\begin{array}{l}\phantom{98)}0065\phantom{8}\\98\overline{)6370}\\\phantom{98)}\underline{\phantom{}588\phantom{9}}\\\phantom{98)9}490\\\phantom{98)}\underline{\phantom{9}490\phantom{}}\\\phantom{98)9999}0\\\end{array}
Find closest multiple of 98 to 490. We see that 5 \times 98 = 490 is the nearest. Now subtract 490 from 490 to get reminder 0. Add 5 to quotient.
\text{Quotient: }65 \text{Reminder: }0
Since 0 is less than 98, 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}