Evaluate
65
Factor
5\times 13
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\begin{array}{l}\phantom{46)}\phantom{1}\\46\overline{)2990}\\\end{array}
Use the 1^{st} digit 2 from dividend 2990
\begin{array}{l}\phantom{46)}0\phantom{2}\\46\overline{)2990}\\\end{array}
Since 2 is less than 46, use the next digit 9 from dividend 2990 and add 0 to the quotient
\begin{array}{l}\phantom{46)}0\phantom{3}\\46\overline{)2990}\\\end{array}
Use the 2^{nd} digit 9 from dividend 2990
\begin{array}{l}\phantom{46)}00\phantom{4}\\46\overline{)2990}\\\end{array}
Since 29 is less than 46, use the next digit 9 from dividend 2990 and add 0 to the quotient
\begin{array}{l}\phantom{46)}00\phantom{5}\\46\overline{)2990}\\\end{array}
Use the 3^{rd} digit 9 from dividend 2990
\begin{array}{l}\phantom{46)}006\phantom{6}\\46\overline{)2990}\\\phantom{46)}\underline{\phantom{}276\phantom{9}}\\\phantom{46)9}23\\\end{array}
Find closest multiple of 46 to 299. We see that 6 \times 46 = 276 is the nearest. Now subtract 276 from 299 to get reminder 23. Add 6 to quotient.
\begin{array}{l}\phantom{46)}006\phantom{7}\\46\overline{)2990}\\\phantom{46)}\underline{\phantom{}276\phantom{9}}\\\phantom{46)9}230\\\end{array}
Use the 4^{th} digit 0 from dividend 2990
\begin{array}{l}\phantom{46)}0065\phantom{8}\\46\overline{)2990}\\\phantom{46)}\underline{\phantom{}276\phantom{9}}\\\phantom{46)9}230\\\phantom{46)}\underline{\phantom{9}230\phantom{}}\\\phantom{46)9999}0\\\end{array}
Find closest multiple of 46 to 230. We see that 5 \times 46 = 230 is the nearest. Now subtract 230 from 230 to get reminder 0. Add 5 to quotient.
\text{Quotient: }65 \text{Reminder: }0
Since 0 is less than 46, 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}