Evaluate
168002835
Factor
3\times 5\times 7\times 11\times 13\times 67\times 167
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\begin{array}{l}\phantom{11)}\phantom{1}\\11\overline{)1848031185}\\\end{array}
Use the 1^{st} digit 1 from dividend 1848031185
\begin{array}{l}\phantom{11)}0\phantom{2}\\11\overline{)1848031185}\\\end{array}
Since 1 is less than 11, use the next digit 8 from dividend 1848031185 and add 0 to the quotient
\begin{array}{l}\phantom{11)}0\phantom{3}\\11\overline{)1848031185}\\\end{array}
Use the 2^{nd} digit 8 from dividend 1848031185
\begin{array}{l}\phantom{11)}01\phantom{4}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}7\\\end{array}
Find closest multiple of 11 to 18. We see that 1 \times 11 = 11 is the nearest. Now subtract 11 from 18 to get reminder 7. Add 1 to quotient.
\begin{array}{l}\phantom{11)}01\phantom{5}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\end{array}
Use the 3^{rd} digit 4 from dividend 1848031185
\begin{array}{l}\phantom{11)}016\phantom{6}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}8\\\end{array}
Find closest multiple of 11 to 74. We see that 6 \times 11 = 66 is the nearest. Now subtract 66 from 74 to get reminder 8. Add 6 to quotient.
\begin{array}{l}\phantom{11)}016\phantom{7}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\end{array}
Use the 4^{th} digit 8 from dividend 1848031185
\begin{array}{l}\phantom{11)}0168\phantom{8}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)9999}0\\\end{array}
Find closest multiple of 11 to 88. We see that 8 \times 11 = 88 is the nearest. Now subtract 88 from 88 to get reminder 0. Add 8 to quotient.
\begin{array}{l}\phantom{11)}0168\phantom{9}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}0\\\end{array}
Use the 5^{th} digit 0 from dividend 1848031185
\begin{array}{l}\phantom{11)}01680\phantom{10}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}0\\\end{array}
Since 0 is less than 11, use the next digit 3 from dividend 1848031185 and add 0 to the quotient
\begin{array}{l}\phantom{11)}01680\phantom{11}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}3\\\end{array}
Use the 6^{th} digit 3 from dividend 1848031185
\begin{array}{l}\phantom{11)}016800\phantom{12}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}3\\\end{array}
Since 3 is less than 11, use the next digit 1 from dividend 1848031185 and add 0 to the quotient
\begin{array}{l}\phantom{11)}016800\phantom{13}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}31\\\end{array}
Use the 7^{th} digit 1 from dividend 1848031185
\begin{array}{l}\phantom{11)}0168002\phantom{14}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}31\\\phantom{11)}\underline{\phantom{99999}22\phantom{999}}\\\phantom{11)999999}9\\\end{array}
Find closest multiple of 11 to 31. We see that 2 \times 11 = 22 is the nearest. Now subtract 22 from 31 to get reminder 9. Add 2 to quotient.
\begin{array}{l}\phantom{11)}0168002\phantom{15}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}31\\\phantom{11)}\underline{\phantom{99999}22\phantom{999}}\\\phantom{11)999999}91\\\end{array}
Use the 8^{th} digit 1 from dividend 1848031185
\begin{array}{l}\phantom{11)}01680028\phantom{16}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}31\\\phantom{11)}\underline{\phantom{99999}22\phantom{999}}\\\phantom{11)999999}91\\\phantom{11)}\underline{\phantom{999999}88\phantom{99}}\\\phantom{11)9999999}3\\\end{array}
Find closest multiple of 11 to 91. We see that 8 \times 11 = 88 is the nearest. Now subtract 88 from 91 to get reminder 3. Add 8 to quotient.
\begin{array}{l}\phantom{11)}01680028\phantom{17}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}31\\\phantom{11)}\underline{\phantom{99999}22\phantom{999}}\\\phantom{11)999999}91\\\phantom{11)}\underline{\phantom{999999}88\phantom{99}}\\\phantom{11)9999999}38\\\end{array}
Use the 9^{th} digit 8 from dividend 1848031185
\begin{array}{l}\phantom{11)}016800283\phantom{18}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}31\\\phantom{11)}\underline{\phantom{99999}22\phantom{999}}\\\phantom{11)999999}91\\\phantom{11)}\underline{\phantom{999999}88\phantom{99}}\\\phantom{11)9999999}38\\\phantom{11)}\underline{\phantom{9999999}33\phantom{9}}\\\phantom{11)99999999}5\\\end{array}
Find closest multiple of 11 to 38. We see that 3 \times 11 = 33 is the nearest. Now subtract 33 from 38 to get reminder 5. Add 3 to quotient.
\begin{array}{l}\phantom{11)}016800283\phantom{19}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}31\\\phantom{11)}\underline{\phantom{99999}22\phantom{999}}\\\phantom{11)999999}91\\\phantom{11)}\underline{\phantom{999999}88\phantom{99}}\\\phantom{11)9999999}38\\\phantom{11)}\underline{\phantom{9999999}33\phantom{9}}\\\phantom{11)99999999}55\\\end{array}
Use the 10^{th} digit 5 from dividend 1848031185
\begin{array}{l}\phantom{11)}0168002835\phantom{20}\\11\overline{)1848031185}\\\phantom{11)}\underline{\phantom{}11\phantom{99999999}}\\\phantom{11)9}74\\\phantom{11)}\underline{\phantom{9}66\phantom{9999999}}\\\phantom{11)99}88\\\phantom{11)}\underline{\phantom{99}88\phantom{999999}}\\\phantom{11)99999}31\\\phantom{11)}\underline{\phantom{99999}22\phantom{999}}\\\phantom{11)999999}91\\\phantom{11)}\underline{\phantom{999999}88\phantom{99}}\\\phantom{11)9999999}38\\\phantom{11)}\underline{\phantom{9999999}33\phantom{9}}\\\phantom{11)99999999}55\\\phantom{11)}\underline{\phantom{99999999}55\phantom{}}\\\phantom{11)9999999999}0\\\end{array}
Find closest multiple of 11 to 55. We see that 5 \times 11 = 55 is the nearest. Now subtract 55 from 55 to get reminder 0. Add 5 to quotient.
\text{Quotient: }168002835 \text{Reminder: }0
Since 0 is less than 11, stop the division. The reminder is 0. The topmost line 0168002835 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 168002835.
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}