Evaluate
\frac{87717347}{35739443}\approx 2.454356857
Factor
\frac{6343 \cdot 13829}{419 \cdot 85297} = 2\frac{16238461}{35739443} = 2.454356857212352
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\begin{array}{l}\phantom{321654987)}\phantom{1}\\321654987\overline{)789456123}\\\end{array}
Use the 1^{st} digit 7 from dividend 789456123
\begin{array}{l}\phantom{321654987)}0\phantom{2}\\321654987\overline{)789456123}\\\end{array}
Since 7 is less than 321654987, use the next digit 8 from dividend 789456123 and add 0 to the quotient
\begin{array}{l}\phantom{321654987)}0\phantom{3}\\321654987\overline{)789456123}\\\end{array}
Use the 2^{nd} digit 8 from dividend 789456123
\begin{array}{l}\phantom{321654987)}00\phantom{4}\\321654987\overline{)789456123}\\\end{array}
Since 78 is less than 321654987, use the next digit 9 from dividend 789456123 and add 0 to the quotient
\begin{array}{l}\phantom{321654987)}00\phantom{5}\\321654987\overline{)789456123}\\\end{array}
Use the 3^{rd} digit 9 from dividend 789456123
\begin{array}{l}\phantom{321654987)}000\phantom{6}\\321654987\overline{)789456123}\\\end{array}
Since 789 is less than 321654987, use the next digit 4 from dividend 789456123 and add 0 to the quotient
\begin{array}{l}\phantom{321654987)}000\phantom{7}\\321654987\overline{)789456123}\\\end{array}
Use the 4^{th} digit 4 from dividend 789456123
\begin{array}{l}\phantom{321654987)}0000\phantom{8}\\321654987\overline{)789456123}\\\end{array}
Since 7894 is less than 321654987, use the next digit 5 from dividend 789456123 and add 0 to the quotient
\begin{array}{l}\phantom{321654987)}0000\phantom{9}\\321654987\overline{)789456123}\\\end{array}
Use the 5^{th} digit 5 from dividend 789456123
\begin{array}{l}\phantom{321654987)}00000\phantom{10}\\321654987\overline{)789456123}\\\end{array}
Since 78945 is less than 321654987, use the next digit 6 from dividend 789456123 and add 0 to the quotient
\begin{array}{l}\phantom{321654987)}00000\phantom{11}\\321654987\overline{)789456123}\\\end{array}
Use the 6^{th} digit 6 from dividend 789456123
\begin{array}{l}\phantom{321654987)}000000\phantom{12}\\321654987\overline{)789456123}\\\end{array}
Since 789456 is less than 321654987, use the next digit 1 from dividend 789456123 and add 0 to the quotient
\begin{array}{l}\phantom{321654987)}000000\phantom{13}\\321654987\overline{)789456123}\\\end{array}
Use the 7^{th} digit 1 from dividend 789456123
\begin{array}{l}\phantom{321654987)}0000000\phantom{14}\\321654987\overline{)789456123}\\\end{array}
Since 7894561 is less than 321654987, use the next digit 2 from dividend 789456123 and add 0 to the quotient
\begin{array}{l}\phantom{321654987)}0000000\phantom{15}\\321654987\overline{)789456123}\\\end{array}
Use the 8^{th} digit 2 from dividend 789456123
\begin{array}{l}\phantom{321654987)}00000000\phantom{16}\\321654987\overline{)789456123}\\\end{array}
Since 78945612 is less than 321654987, use the next digit 3 from dividend 789456123 and add 0 to the quotient
\begin{array}{l}\phantom{321654987)}00000000\phantom{17}\\321654987\overline{)789456123}\\\end{array}
Use the 9^{th} digit 3 from dividend 789456123
\begin{array}{l}\phantom{321654987)}000000002\phantom{18}\\321654987\overline{)789456123}\\\phantom{321654987)}\underline{\phantom{}643309974\phantom{}}\\\phantom{321654987)}146146149\\\end{array}
Find closest multiple of 321654987 to 789456123. We see that 2 \times 321654987 = 643309974 is the nearest. Now subtract 643309974 from 789456123 to get reminder 146146149. Add 2 to quotient.
\text{Quotient: }2 \text{Reminder: }146146149
Since 146146149 is less than 321654987, stop the division. The reminder is 146146149. The topmost line 000000002 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2.
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}