Evaluate
\frac{40731}{89}\approx 457.651685393
Factor
\frac{3 \cdot 13577}{89} = 457\frac{58}{89} = 457.65168539325845
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\begin{array}{l}\phantom{89)}\phantom{1}\\89\overline{)40731}\\\end{array}
Use the 1^{st} digit 4 from dividend 40731
\begin{array}{l}\phantom{89)}0\phantom{2}\\89\overline{)40731}\\\end{array}
Since 4 is less than 89, use the next digit 0 from dividend 40731 and add 0 to the quotient
\begin{array}{l}\phantom{89)}0\phantom{3}\\89\overline{)40731}\\\end{array}
Use the 2^{nd} digit 0 from dividend 40731
\begin{array}{l}\phantom{89)}00\phantom{4}\\89\overline{)40731}\\\end{array}
Since 40 is less than 89, use the next digit 7 from dividend 40731 and add 0 to the quotient
\begin{array}{l}\phantom{89)}00\phantom{5}\\89\overline{)40731}\\\end{array}
Use the 3^{rd} digit 7 from dividend 40731
\begin{array}{l}\phantom{89)}004\phantom{6}\\89\overline{)40731}\\\phantom{89)}\underline{\phantom{}356\phantom{99}}\\\phantom{89)9}51\\\end{array}
Find closest multiple of 89 to 407. We see that 4 \times 89 = 356 is the nearest. Now subtract 356 from 407 to get reminder 51. Add 4 to quotient.
\begin{array}{l}\phantom{89)}004\phantom{7}\\89\overline{)40731}\\\phantom{89)}\underline{\phantom{}356\phantom{99}}\\\phantom{89)9}513\\\end{array}
Use the 4^{th} digit 3 from dividend 40731
\begin{array}{l}\phantom{89)}0045\phantom{8}\\89\overline{)40731}\\\phantom{89)}\underline{\phantom{}356\phantom{99}}\\\phantom{89)9}513\\\phantom{89)}\underline{\phantom{9}445\phantom{9}}\\\phantom{89)99}68\\\end{array}
Find closest multiple of 89 to 513. We see that 5 \times 89 = 445 is the nearest. Now subtract 445 from 513 to get reminder 68. Add 5 to quotient.
\begin{array}{l}\phantom{89)}0045\phantom{9}\\89\overline{)40731}\\\phantom{89)}\underline{\phantom{}356\phantom{99}}\\\phantom{89)9}513\\\phantom{89)}\underline{\phantom{9}445\phantom{9}}\\\phantom{89)99}681\\\end{array}
Use the 5^{th} digit 1 from dividend 40731
\begin{array}{l}\phantom{89)}00457\phantom{10}\\89\overline{)40731}\\\phantom{89)}\underline{\phantom{}356\phantom{99}}\\\phantom{89)9}513\\\phantom{89)}\underline{\phantom{9}445\phantom{9}}\\\phantom{89)99}681\\\phantom{89)}\underline{\phantom{99}623\phantom{}}\\\phantom{89)999}58\\\end{array}
Find closest multiple of 89 to 681. We see that 7 \times 89 = 623 is the nearest. Now subtract 623 from 681 to get reminder 58. Add 7 to quotient.
\text{Quotient: }457 \text{Reminder: }58
Since 58 is less than 89, stop the division. The reminder is 58. The topmost line 00457 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 457.
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}