Evaluate
\frac{50505}{31}\approx 1629.193548387
Factor
\frac{3 \cdot 5 \cdot 7 \cdot 13 \cdot 37}{31} = 1629\frac{6}{31} = 1629.1935483870968
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\begin{array}{l}\phantom{31)}\phantom{1}\\31\overline{)50505}\\\end{array}
Use the 1^{st} digit 5 from dividend 50505
\begin{array}{l}\phantom{31)}0\phantom{2}\\31\overline{)50505}\\\end{array}
Since 5 is less than 31, use the next digit 0 from dividend 50505 and add 0 to the quotient
\begin{array}{l}\phantom{31)}0\phantom{3}\\31\overline{)50505}\\\end{array}
Use the 2^{nd} digit 0 from dividend 50505
\begin{array}{l}\phantom{31)}01\phantom{4}\\31\overline{)50505}\\\phantom{31)}\underline{\phantom{}31\phantom{999}}\\\phantom{31)}19\\\end{array}
Find closest multiple of 31 to 50. We see that 1 \times 31 = 31 is the nearest. Now subtract 31 from 50 to get reminder 19. Add 1 to quotient.
\begin{array}{l}\phantom{31)}01\phantom{5}\\31\overline{)50505}\\\phantom{31)}\underline{\phantom{}31\phantom{999}}\\\phantom{31)}195\\\end{array}
Use the 3^{rd} digit 5 from dividend 50505
\begin{array}{l}\phantom{31)}016\phantom{6}\\31\overline{)50505}\\\phantom{31)}\underline{\phantom{}31\phantom{999}}\\\phantom{31)}195\\\phantom{31)}\underline{\phantom{}186\phantom{99}}\\\phantom{31)99}9\\\end{array}
Find closest multiple of 31 to 195. We see that 6 \times 31 = 186 is the nearest. Now subtract 186 from 195 to get reminder 9. Add 6 to quotient.
\begin{array}{l}\phantom{31)}016\phantom{7}\\31\overline{)50505}\\\phantom{31)}\underline{\phantom{}31\phantom{999}}\\\phantom{31)}195\\\phantom{31)}\underline{\phantom{}186\phantom{99}}\\\phantom{31)99}90\\\end{array}
Use the 4^{th} digit 0 from dividend 50505
\begin{array}{l}\phantom{31)}0162\phantom{8}\\31\overline{)50505}\\\phantom{31)}\underline{\phantom{}31\phantom{999}}\\\phantom{31)}195\\\phantom{31)}\underline{\phantom{}186\phantom{99}}\\\phantom{31)99}90\\\phantom{31)}\underline{\phantom{99}62\phantom{9}}\\\phantom{31)99}28\\\end{array}
Find closest multiple of 31 to 90. We see that 2 \times 31 = 62 is the nearest. Now subtract 62 from 90 to get reminder 28. Add 2 to quotient.
\begin{array}{l}\phantom{31)}0162\phantom{9}\\31\overline{)50505}\\\phantom{31)}\underline{\phantom{}31\phantom{999}}\\\phantom{31)}195\\\phantom{31)}\underline{\phantom{}186\phantom{99}}\\\phantom{31)99}90\\\phantom{31)}\underline{\phantom{99}62\phantom{9}}\\\phantom{31)99}285\\\end{array}
Use the 5^{th} digit 5 from dividend 50505
\begin{array}{l}\phantom{31)}01629\phantom{10}\\31\overline{)50505}\\\phantom{31)}\underline{\phantom{}31\phantom{999}}\\\phantom{31)}195\\\phantom{31)}\underline{\phantom{}186\phantom{99}}\\\phantom{31)99}90\\\phantom{31)}\underline{\phantom{99}62\phantom{9}}\\\phantom{31)99}285\\\phantom{31)}\underline{\phantom{99}279\phantom{}}\\\phantom{31)9999}6\\\end{array}
Find closest multiple of 31 to 285. We see that 9 \times 31 = 279 is the nearest. Now subtract 279 from 285 to get reminder 6. Add 9 to quotient.
\text{Quotient: }1629 \text{Reminder: }6
Since 6 is less than 31, stop the division. The reminder is 6. The topmost line 01629 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1629.
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}