Evaluate
\frac{300000}{73}\approx 4109.589041096
Factor
\frac{2 ^ {5} \cdot 3 \cdot 5 ^ {5}}{73} = 4109\frac{43}{73} = 4109.58904109589
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\begin{array}{l}\phantom{365)}\phantom{1}\\365\overline{)1500000}\\\end{array}
Use the 1^{st} digit 1 from dividend 1500000
\begin{array}{l}\phantom{365)}0\phantom{2}\\365\overline{)1500000}\\\end{array}
Since 1 is less than 365, use the next digit 5 from dividend 1500000 and add 0 to the quotient
\begin{array}{l}\phantom{365)}0\phantom{3}\\365\overline{)1500000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1500000
\begin{array}{l}\phantom{365)}00\phantom{4}\\365\overline{)1500000}\\\end{array}
Since 15 is less than 365, use the next digit 0 from dividend 1500000 and add 0 to the quotient
\begin{array}{l}\phantom{365)}00\phantom{5}\\365\overline{)1500000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1500000
\begin{array}{l}\phantom{365)}000\phantom{6}\\365\overline{)1500000}\\\end{array}
Since 150 is less than 365, use the next digit 0 from dividend 1500000 and add 0 to the quotient
\begin{array}{l}\phantom{365)}000\phantom{7}\\365\overline{)1500000}\\\end{array}
Use the 4^{th} digit 0 from dividend 1500000
\begin{array}{l}\phantom{365)}0004\phantom{8}\\365\overline{)1500000}\\\phantom{365)}\underline{\phantom{}1460\phantom{999}}\\\phantom{365)99}40\\\end{array}
Find closest multiple of 365 to 1500. We see that 4 \times 365 = 1460 is the nearest. Now subtract 1460 from 1500 to get reminder 40. Add 4 to quotient.
\begin{array}{l}\phantom{365)}0004\phantom{9}\\365\overline{)1500000}\\\phantom{365)}\underline{\phantom{}1460\phantom{999}}\\\phantom{365)99}400\\\end{array}
Use the 5^{th} digit 0 from dividend 1500000
\begin{array}{l}\phantom{365)}00041\phantom{10}\\365\overline{)1500000}\\\phantom{365)}\underline{\phantom{}1460\phantom{999}}\\\phantom{365)99}400\\\phantom{365)}\underline{\phantom{99}365\phantom{99}}\\\phantom{365)999}35\\\end{array}
Find closest multiple of 365 to 400. We see that 1 \times 365 = 365 is the nearest. Now subtract 365 from 400 to get reminder 35. Add 1 to quotient.
\begin{array}{l}\phantom{365)}00041\phantom{11}\\365\overline{)1500000}\\\phantom{365)}\underline{\phantom{}1460\phantom{999}}\\\phantom{365)99}400\\\phantom{365)}\underline{\phantom{99}365\phantom{99}}\\\phantom{365)999}350\\\end{array}
Use the 6^{th} digit 0 from dividend 1500000
\begin{array}{l}\phantom{365)}000410\phantom{12}\\365\overline{)1500000}\\\phantom{365)}\underline{\phantom{}1460\phantom{999}}\\\phantom{365)99}400\\\phantom{365)}\underline{\phantom{99}365\phantom{99}}\\\phantom{365)999}350\\\end{array}
Since 350 is less than 365, use the next digit 0 from dividend 1500000 and add 0 to the quotient
\begin{array}{l}\phantom{365)}000410\phantom{13}\\365\overline{)1500000}\\\phantom{365)}\underline{\phantom{}1460\phantom{999}}\\\phantom{365)99}400\\\phantom{365)}\underline{\phantom{99}365\phantom{99}}\\\phantom{365)999}3500\\\end{array}
Use the 7^{th} digit 0 from dividend 1500000
\begin{array}{l}\phantom{365)}0004109\phantom{14}\\365\overline{)1500000}\\\phantom{365)}\underline{\phantom{}1460\phantom{999}}\\\phantom{365)99}400\\\phantom{365)}\underline{\phantom{99}365\phantom{99}}\\\phantom{365)999}3500\\\phantom{365)}\underline{\phantom{999}3285\phantom{}}\\\phantom{365)9999}215\\\end{array}
Find closest multiple of 365 to 3500. We see that 9 \times 365 = 3285 is the nearest. Now subtract 3285 from 3500 to get reminder 215. Add 9 to quotient.
\text{Quotient: }4109 \text{Reminder: }215
Since 215 is less than 365, stop the division. The reminder is 215. The topmost line 0004109 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4109.
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}