Evaluate
\frac{86319}{1321}\approx 65.343679031
Factor
\frac{3 ^ {3} \cdot 23 \cdot 139}{1321} = 65\frac{454}{1321} = 65.3436790310371
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\begin{array}{l}\phantom{1321)}\phantom{1}\\1321\overline{)86319}\\\end{array}
Use the 1^{st} digit 8 from dividend 86319
\begin{array}{l}\phantom{1321)}0\phantom{2}\\1321\overline{)86319}\\\end{array}
Since 8 is less than 1321, use the next digit 6 from dividend 86319 and add 0 to the quotient
\begin{array}{l}\phantom{1321)}0\phantom{3}\\1321\overline{)86319}\\\end{array}
Use the 2^{nd} digit 6 from dividend 86319
\begin{array}{l}\phantom{1321)}00\phantom{4}\\1321\overline{)86319}\\\end{array}
Since 86 is less than 1321, use the next digit 3 from dividend 86319 and add 0 to the quotient
\begin{array}{l}\phantom{1321)}00\phantom{5}\\1321\overline{)86319}\\\end{array}
Use the 3^{rd} digit 3 from dividend 86319
\begin{array}{l}\phantom{1321)}000\phantom{6}\\1321\overline{)86319}\\\end{array}
Since 863 is less than 1321, use the next digit 1 from dividend 86319 and add 0 to the quotient
\begin{array}{l}\phantom{1321)}000\phantom{7}\\1321\overline{)86319}\\\end{array}
Use the 4^{th} digit 1 from dividend 86319
\begin{array}{l}\phantom{1321)}0006\phantom{8}\\1321\overline{)86319}\\\phantom{1321)}\underline{\phantom{}7926\phantom{9}}\\\phantom{1321)9}705\\\end{array}
Find closest multiple of 1321 to 8631. We see that 6 \times 1321 = 7926 is the nearest. Now subtract 7926 from 8631 to get reminder 705. Add 6 to quotient.
\begin{array}{l}\phantom{1321)}0006\phantom{9}\\1321\overline{)86319}\\\phantom{1321)}\underline{\phantom{}7926\phantom{9}}\\\phantom{1321)9}7059\\\end{array}
Use the 5^{th} digit 9 from dividend 86319
\begin{array}{l}\phantom{1321)}00065\phantom{10}\\1321\overline{)86319}\\\phantom{1321)}\underline{\phantom{}7926\phantom{9}}\\\phantom{1321)9}7059\\\phantom{1321)}\underline{\phantom{9}6605\phantom{}}\\\phantom{1321)99}454\\\end{array}
Find closest multiple of 1321 to 7059. We see that 5 \times 1321 = 6605 is the nearest. Now subtract 6605 from 7059 to get reminder 454. Add 5 to quotient.
\text{Quotient: }65 \text{Reminder: }454
Since 454 is less than 1321, stop the division. The reminder is 454. The topmost line 00065 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}