Evaluate
\frac{45315169}{8546}\approx 5302.500468055
Factor
\frac{45315169}{2 \cdot 4273} = 5302\frac{4277}{8546} = 5302.50046805523
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\begin{array}{l}\phantom{8546)}\phantom{1}\\8546\overline{)45315169}\\\end{array}
Use the 1^{st} digit 4 from dividend 45315169
\begin{array}{l}\phantom{8546)}0\phantom{2}\\8546\overline{)45315169}\\\end{array}
Since 4 is less than 8546, use the next digit 5 from dividend 45315169 and add 0 to the quotient
\begin{array}{l}\phantom{8546)}0\phantom{3}\\8546\overline{)45315169}\\\end{array}
Use the 2^{nd} digit 5 from dividend 45315169
\begin{array}{l}\phantom{8546)}00\phantom{4}\\8546\overline{)45315169}\\\end{array}
Since 45 is less than 8546, use the next digit 3 from dividend 45315169 and add 0 to the quotient
\begin{array}{l}\phantom{8546)}00\phantom{5}\\8546\overline{)45315169}\\\end{array}
Use the 3^{rd} digit 3 from dividend 45315169
\begin{array}{l}\phantom{8546)}000\phantom{6}\\8546\overline{)45315169}\\\end{array}
Since 453 is less than 8546, use the next digit 1 from dividend 45315169 and add 0 to the quotient
\begin{array}{l}\phantom{8546)}000\phantom{7}\\8546\overline{)45315169}\\\end{array}
Use the 4^{th} digit 1 from dividend 45315169
\begin{array}{l}\phantom{8546)}0000\phantom{8}\\8546\overline{)45315169}\\\end{array}
Since 4531 is less than 8546, use the next digit 5 from dividend 45315169 and add 0 to the quotient
\begin{array}{l}\phantom{8546)}0000\phantom{9}\\8546\overline{)45315169}\\\end{array}
Use the 5^{th} digit 5 from dividend 45315169
\begin{array}{l}\phantom{8546)}00005\phantom{10}\\8546\overline{)45315169}\\\phantom{8546)}\underline{\phantom{}42730\phantom{999}}\\\phantom{8546)9}2585\\\end{array}
Find closest multiple of 8546 to 45315. We see that 5 \times 8546 = 42730 is the nearest. Now subtract 42730 from 45315 to get reminder 2585. Add 5 to quotient.
\begin{array}{l}\phantom{8546)}00005\phantom{11}\\8546\overline{)45315169}\\\phantom{8546)}\underline{\phantom{}42730\phantom{999}}\\\phantom{8546)9}25851\\\end{array}
Use the 6^{th} digit 1 from dividend 45315169
\begin{array}{l}\phantom{8546)}000053\phantom{12}\\8546\overline{)45315169}\\\phantom{8546)}\underline{\phantom{}42730\phantom{999}}\\\phantom{8546)9}25851\\\phantom{8546)}\underline{\phantom{9}25638\phantom{99}}\\\phantom{8546)999}213\\\end{array}
Find closest multiple of 8546 to 25851. We see that 3 \times 8546 = 25638 is the nearest. Now subtract 25638 from 25851 to get reminder 213. Add 3 to quotient.
\begin{array}{l}\phantom{8546)}000053\phantom{13}\\8546\overline{)45315169}\\\phantom{8546)}\underline{\phantom{}42730\phantom{999}}\\\phantom{8546)9}25851\\\phantom{8546)}\underline{\phantom{9}25638\phantom{99}}\\\phantom{8546)999}2136\\\end{array}
Use the 7^{th} digit 6 from dividend 45315169
\begin{array}{l}\phantom{8546)}0000530\phantom{14}\\8546\overline{)45315169}\\\phantom{8546)}\underline{\phantom{}42730\phantom{999}}\\\phantom{8546)9}25851\\\phantom{8546)}\underline{\phantom{9}25638\phantom{99}}\\\phantom{8546)999}2136\\\end{array}
Since 2136 is less than 8546, use the next digit 9 from dividend 45315169 and add 0 to the quotient
\begin{array}{l}\phantom{8546)}0000530\phantom{15}\\8546\overline{)45315169}\\\phantom{8546)}\underline{\phantom{}42730\phantom{999}}\\\phantom{8546)9}25851\\\phantom{8546)}\underline{\phantom{9}25638\phantom{99}}\\\phantom{8546)999}21369\\\end{array}
Use the 8^{th} digit 9 from dividend 45315169
\begin{array}{l}\phantom{8546)}00005302\phantom{16}\\8546\overline{)45315169}\\\phantom{8546)}\underline{\phantom{}42730\phantom{999}}\\\phantom{8546)9}25851\\\phantom{8546)}\underline{\phantom{9}25638\phantom{99}}\\\phantom{8546)999}21369\\\phantom{8546)}\underline{\phantom{999}17092\phantom{}}\\\phantom{8546)9999}4277\\\end{array}
Find closest multiple of 8546 to 21369. We see that 2 \times 8546 = 17092 is the nearest. Now subtract 17092 from 21369 to get reminder 4277. Add 2 to quotient.
\text{Quotient: }5302 \text{Reminder: }4277
Since 4277 is less than 8546, stop the division. The reminder is 4277. The topmost line 00005302 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 5302.
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}