Evaluate
\frac{122389}{267}\approx 458.38576779
Factor
\frac{122389}{3 \cdot 89} = 458\frac{103}{267} = 458.38576779026215
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\begin{array}{l}\phantom{267)}\phantom{1}\\267\overline{)122389}\\\end{array}
Use the 1^{st} digit 1 from dividend 122389
\begin{array}{l}\phantom{267)}0\phantom{2}\\267\overline{)122389}\\\end{array}
Since 1 is less than 267, use the next digit 2 from dividend 122389 and add 0 to the quotient
\begin{array}{l}\phantom{267)}0\phantom{3}\\267\overline{)122389}\\\end{array}
Use the 2^{nd} digit 2 from dividend 122389
\begin{array}{l}\phantom{267)}00\phantom{4}\\267\overline{)122389}\\\end{array}
Since 12 is less than 267, use the next digit 2 from dividend 122389 and add 0 to the quotient
\begin{array}{l}\phantom{267)}00\phantom{5}\\267\overline{)122389}\\\end{array}
Use the 3^{rd} digit 2 from dividend 122389
\begin{array}{l}\phantom{267)}000\phantom{6}\\267\overline{)122389}\\\end{array}
Since 122 is less than 267, use the next digit 3 from dividend 122389 and add 0 to the quotient
\begin{array}{l}\phantom{267)}000\phantom{7}\\267\overline{)122389}\\\end{array}
Use the 4^{th} digit 3 from dividend 122389
\begin{array}{l}\phantom{267)}0004\phantom{8}\\267\overline{)122389}\\\phantom{267)}\underline{\phantom{}1068\phantom{99}}\\\phantom{267)9}155\\\end{array}
Find closest multiple of 267 to 1223. We see that 4 \times 267 = 1068 is the nearest. Now subtract 1068 from 1223 to get reminder 155. Add 4 to quotient.
\begin{array}{l}\phantom{267)}0004\phantom{9}\\267\overline{)122389}\\\phantom{267)}\underline{\phantom{}1068\phantom{99}}\\\phantom{267)9}1558\\\end{array}
Use the 5^{th} digit 8 from dividend 122389
\begin{array}{l}\phantom{267)}00045\phantom{10}\\267\overline{)122389}\\\phantom{267)}\underline{\phantom{}1068\phantom{99}}\\\phantom{267)9}1558\\\phantom{267)}\underline{\phantom{9}1335\phantom{9}}\\\phantom{267)99}223\\\end{array}
Find closest multiple of 267 to 1558. We see that 5 \times 267 = 1335 is the nearest. Now subtract 1335 from 1558 to get reminder 223. Add 5 to quotient.
\begin{array}{l}\phantom{267)}00045\phantom{11}\\267\overline{)122389}\\\phantom{267)}\underline{\phantom{}1068\phantom{99}}\\\phantom{267)9}1558\\\phantom{267)}\underline{\phantom{9}1335\phantom{9}}\\\phantom{267)99}2239\\\end{array}
Use the 6^{th} digit 9 from dividend 122389
\begin{array}{l}\phantom{267)}000458\phantom{12}\\267\overline{)122389}\\\phantom{267)}\underline{\phantom{}1068\phantom{99}}\\\phantom{267)9}1558\\\phantom{267)}\underline{\phantom{9}1335\phantom{9}}\\\phantom{267)99}2239\\\phantom{267)}\underline{\phantom{99}2136\phantom{}}\\\phantom{267)999}103\\\end{array}
Find closest multiple of 267 to 2239. We see that 8 \times 267 = 2136 is the nearest. Now subtract 2136 from 2239 to get reminder 103. Add 8 to quotient.
\text{Quotient: }458 \text{Reminder: }103
Since 103 is less than 267, stop the division. The reminder is 103. The topmost line 000458 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 458.
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}