Evaluate
\frac{3120}{17}\approx 183.529411765
Factor
\frac{2 ^ {4} \cdot 3 \cdot 5 \cdot 13}{17} = 183\frac{9}{17} = 183.52941176470588
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\begin{array}{l}\phantom{85)}\phantom{1}\\85\overline{)15600}\\\end{array}
Use the 1^{st} digit 1 from dividend 15600
\begin{array}{l}\phantom{85)}0\phantom{2}\\85\overline{)15600}\\\end{array}
Since 1 is less than 85, use the next digit 5 from dividend 15600 and add 0 to the quotient
\begin{array}{l}\phantom{85)}0\phantom{3}\\85\overline{)15600}\\\end{array}
Use the 2^{nd} digit 5 from dividend 15600
\begin{array}{l}\phantom{85)}00\phantom{4}\\85\overline{)15600}\\\end{array}
Since 15 is less than 85, use the next digit 6 from dividend 15600 and add 0 to the quotient
\begin{array}{l}\phantom{85)}00\phantom{5}\\85\overline{)15600}\\\end{array}
Use the 3^{rd} digit 6 from dividend 15600
\begin{array}{l}\phantom{85)}001\phantom{6}\\85\overline{)15600}\\\phantom{85)}\underline{\phantom{9}85\phantom{99}}\\\phantom{85)9}71\\\end{array}
Find closest multiple of 85 to 156. We see that 1 \times 85 = 85 is the nearest. Now subtract 85 from 156 to get reminder 71. Add 1 to quotient.
\begin{array}{l}\phantom{85)}001\phantom{7}\\85\overline{)15600}\\\phantom{85)}\underline{\phantom{9}85\phantom{99}}\\\phantom{85)9}710\\\end{array}
Use the 4^{th} digit 0 from dividend 15600
\begin{array}{l}\phantom{85)}0018\phantom{8}\\85\overline{)15600}\\\phantom{85)}\underline{\phantom{9}85\phantom{99}}\\\phantom{85)9}710\\\phantom{85)}\underline{\phantom{9}680\phantom{9}}\\\phantom{85)99}30\\\end{array}
Find closest multiple of 85 to 710. We see that 8 \times 85 = 680 is the nearest. Now subtract 680 from 710 to get reminder 30. Add 8 to quotient.
\begin{array}{l}\phantom{85)}0018\phantom{9}\\85\overline{)15600}\\\phantom{85)}\underline{\phantom{9}85\phantom{99}}\\\phantom{85)9}710\\\phantom{85)}\underline{\phantom{9}680\phantom{9}}\\\phantom{85)99}300\\\end{array}
Use the 5^{th} digit 0 from dividend 15600
\begin{array}{l}\phantom{85)}00183\phantom{10}\\85\overline{)15600}\\\phantom{85)}\underline{\phantom{9}85\phantom{99}}\\\phantom{85)9}710\\\phantom{85)}\underline{\phantom{9}680\phantom{9}}\\\phantom{85)99}300\\\phantom{85)}\underline{\phantom{99}255\phantom{}}\\\phantom{85)999}45\\\end{array}
Find closest multiple of 85 to 300. We see that 3 \times 85 = 255 is the nearest. Now subtract 255 from 300 to get reminder 45. Add 3 to quotient.
\text{Quotient: }183 \text{Reminder: }45
Since 45 is less than 85, stop the division. The reminder is 45. The topmost line 00183 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 183.
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}