Evaluate
506
Factor
2\times 11\times 23
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\begin{array}{l}\phantom{3497)}\phantom{1}\\3497\overline{)1769482}\\\end{array}
Use the 1^{st} digit 1 from dividend 1769482
\begin{array}{l}\phantom{3497)}0\phantom{2}\\3497\overline{)1769482}\\\end{array}
Since 1 is less than 3497, use the next digit 7 from dividend 1769482 and add 0 to the quotient
\begin{array}{l}\phantom{3497)}0\phantom{3}\\3497\overline{)1769482}\\\end{array}
Use the 2^{nd} digit 7 from dividend 1769482
\begin{array}{l}\phantom{3497)}00\phantom{4}\\3497\overline{)1769482}\\\end{array}
Since 17 is less than 3497, use the next digit 6 from dividend 1769482 and add 0 to the quotient
\begin{array}{l}\phantom{3497)}00\phantom{5}\\3497\overline{)1769482}\\\end{array}
Use the 3^{rd} digit 6 from dividend 1769482
\begin{array}{l}\phantom{3497)}000\phantom{6}\\3497\overline{)1769482}\\\end{array}
Since 176 is less than 3497, use the next digit 9 from dividend 1769482 and add 0 to the quotient
\begin{array}{l}\phantom{3497)}000\phantom{7}\\3497\overline{)1769482}\\\end{array}
Use the 4^{th} digit 9 from dividend 1769482
\begin{array}{l}\phantom{3497)}0000\phantom{8}\\3497\overline{)1769482}\\\end{array}
Since 1769 is less than 3497, use the next digit 4 from dividend 1769482 and add 0 to the quotient
\begin{array}{l}\phantom{3497)}0000\phantom{9}\\3497\overline{)1769482}\\\end{array}
Use the 5^{th} digit 4 from dividend 1769482
\begin{array}{l}\phantom{3497)}00005\phantom{10}\\3497\overline{)1769482}\\\phantom{3497)}\underline{\phantom{}17485\phantom{99}}\\\phantom{3497)99}209\\\end{array}
Find closest multiple of 3497 to 17694. We see that 5 \times 3497 = 17485 is the nearest. Now subtract 17485 from 17694 to get reminder 209. Add 5 to quotient.
\begin{array}{l}\phantom{3497)}00005\phantom{11}\\3497\overline{)1769482}\\\phantom{3497)}\underline{\phantom{}17485\phantom{99}}\\\phantom{3497)99}2098\\\end{array}
Use the 6^{th} digit 8 from dividend 1769482
\begin{array}{l}\phantom{3497)}000050\phantom{12}\\3497\overline{)1769482}\\\phantom{3497)}\underline{\phantom{}17485\phantom{99}}\\\phantom{3497)99}2098\\\end{array}
Since 2098 is less than 3497, use the next digit 2 from dividend 1769482 and add 0 to the quotient
\begin{array}{l}\phantom{3497)}000050\phantom{13}\\3497\overline{)1769482}\\\phantom{3497)}\underline{\phantom{}17485\phantom{99}}\\\phantom{3497)99}20982\\\end{array}
Use the 7^{th} digit 2 from dividend 1769482
\begin{array}{l}\phantom{3497)}0000506\phantom{14}\\3497\overline{)1769482}\\\phantom{3497)}\underline{\phantom{}17485\phantom{99}}\\\phantom{3497)99}20982\\\phantom{3497)}\underline{\phantom{99}20982\phantom{}}\\\phantom{3497)9999999}0\\\end{array}
Find closest multiple of 3497 to 20982. We see that 6 \times 3497 = 20982 is the nearest. Now subtract 20982 from 20982 to get reminder 0. Add 6 to quotient.
\text{Quotient: }506 \text{Reminder: }0
Since 0 is less than 3497, stop the division. The reminder is 0. The topmost line 0000506 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 506.
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}