Evaluate
698
Factor
2\times 349
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\begin{array}{l}\phantom{65)}\phantom{1}\\65\overline{)45370}\\\end{array}
Use the 1^{st} digit 4 from dividend 45370
\begin{array}{l}\phantom{65)}0\phantom{2}\\65\overline{)45370}\\\end{array}
Since 4 is less than 65, use the next digit 5 from dividend 45370 and add 0 to the quotient
\begin{array}{l}\phantom{65)}0\phantom{3}\\65\overline{)45370}\\\end{array}
Use the 2^{nd} digit 5 from dividend 45370
\begin{array}{l}\phantom{65)}00\phantom{4}\\65\overline{)45370}\\\end{array}
Since 45 is less than 65, use the next digit 3 from dividend 45370 and add 0 to the quotient
\begin{array}{l}\phantom{65)}00\phantom{5}\\65\overline{)45370}\\\end{array}
Use the 3^{rd} digit 3 from dividend 45370
\begin{array}{l}\phantom{65)}006\phantom{6}\\65\overline{)45370}\\\phantom{65)}\underline{\phantom{}390\phantom{99}}\\\phantom{65)9}63\\\end{array}
Find closest multiple of 65 to 453. We see that 6 \times 65 = 390 is the nearest. Now subtract 390 from 453 to get reminder 63. Add 6 to quotient.
\begin{array}{l}\phantom{65)}006\phantom{7}\\65\overline{)45370}\\\phantom{65)}\underline{\phantom{}390\phantom{99}}\\\phantom{65)9}637\\\end{array}
Use the 4^{th} digit 7 from dividend 45370
\begin{array}{l}\phantom{65)}0069\phantom{8}\\65\overline{)45370}\\\phantom{65)}\underline{\phantom{}390\phantom{99}}\\\phantom{65)9}637\\\phantom{65)}\underline{\phantom{9}585\phantom{9}}\\\phantom{65)99}52\\\end{array}
Find closest multiple of 65 to 637. We see that 9 \times 65 = 585 is the nearest. Now subtract 585 from 637 to get reminder 52. Add 9 to quotient.
\begin{array}{l}\phantom{65)}0069\phantom{9}\\65\overline{)45370}\\\phantom{65)}\underline{\phantom{}390\phantom{99}}\\\phantom{65)9}637\\\phantom{65)}\underline{\phantom{9}585\phantom{9}}\\\phantom{65)99}520\\\end{array}
Use the 5^{th} digit 0 from dividend 45370
\begin{array}{l}\phantom{65)}00698\phantom{10}\\65\overline{)45370}\\\phantom{65)}\underline{\phantom{}390\phantom{99}}\\\phantom{65)9}637\\\phantom{65)}\underline{\phantom{9}585\phantom{9}}\\\phantom{65)99}520\\\phantom{65)}\underline{\phantom{99}520\phantom{}}\\\phantom{65)99999}0\\\end{array}
Find closest multiple of 65 to 520. We see that 8 \times 65 = 520 is the nearest. Now subtract 520 from 520 to get reminder 0. Add 8 to quotient.
\text{Quotient: }698 \text{Reminder: }0
Since 0 is less than 65, stop the division. The reminder is 0. The topmost line 00698 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 698.
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}