Evaluate
442462
Factor
2\times 197\times 1123
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\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)7964316}\\\end{array}
Use the 1^{st} digit 7 from dividend 7964316
\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)7964316}\\\end{array}
Since 7 is less than 18, use the next digit 9 from dividend 7964316 and add 0 to the quotient
\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)7964316}\\\end{array}
Use the 2^{nd} digit 9 from dividend 7964316
\begin{array}{l}\phantom{18)}04\phantom{4}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}7\\\end{array}
Find closest multiple of 18 to 79. We see that 4 \times 18 = 72 is the nearest. Now subtract 72 from 79 to get reminder 7. Add 4 to quotient.
\begin{array}{l}\phantom{18)}04\phantom{5}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\end{array}
Use the 3^{rd} digit 6 from dividend 7964316
\begin{array}{l}\phantom{18)}044\phantom{6}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}4\\\end{array}
Find closest multiple of 18 to 76. We see that 4 \times 18 = 72 is the nearest. Now subtract 72 from 76 to get reminder 4. Add 4 to quotient.
\begin{array}{l}\phantom{18)}044\phantom{7}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}44\\\end{array}
Use the 4^{th} digit 4 from dividend 7964316
\begin{array}{l}\phantom{18)}0442\phantom{8}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}44\\\phantom{18)}\underline{\phantom{99}36\phantom{999}}\\\phantom{18)999}8\\\end{array}
Find closest multiple of 18 to 44. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 44 to get reminder 8. Add 2 to quotient.
\begin{array}{l}\phantom{18)}0442\phantom{9}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}44\\\phantom{18)}\underline{\phantom{99}36\phantom{999}}\\\phantom{18)999}83\\\end{array}
Use the 5^{th} digit 3 from dividend 7964316
\begin{array}{l}\phantom{18)}04424\phantom{10}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}44\\\phantom{18)}\underline{\phantom{99}36\phantom{999}}\\\phantom{18)999}83\\\phantom{18)}\underline{\phantom{999}72\phantom{99}}\\\phantom{18)999}11\\\end{array}
Find closest multiple of 18 to 83. We see that 4 \times 18 = 72 is the nearest. Now subtract 72 from 83 to get reminder 11. Add 4 to quotient.
\begin{array}{l}\phantom{18)}04424\phantom{11}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}44\\\phantom{18)}\underline{\phantom{99}36\phantom{999}}\\\phantom{18)999}83\\\phantom{18)}\underline{\phantom{999}72\phantom{99}}\\\phantom{18)999}111\\\end{array}
Use the 6^{th} digit 1 from dividend 7964316
\begin{array}{l}\phantom{18)}044246\phantom{12}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}44\\\phantom{18)}\underline{\phantom{99}36\phantom{999}}\\\phantom{18)999}83\\\phantom{18)}\underline{\phantom{999}72\phantom{99}}\\\phantom{18)999}111\\\phantom{18)}\underline{\phantom{999}108\phantom{9}}\\\phantom{18)99999}3\\\end{array}
Find closest multiple of 18 to 111. We see that 6 \times 18 = 108 is the nearest. Now subtract 108 from 111 to get reminder 3. Add 6 to quotient.
\begin{array}{l}\phantom{18)}044246\phantom{13}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}44\\\phantom{18)}\underline{\phantom{99}36\phantom{999}}\\\phantom{18)999}83\\\phantom{18)}\underline{\phantom{999}72\phantom{99}}\\\phantom{18)999}111\\\phantom{18)}\underline{\phantom{999}108\phantom{9}}\\\phantom{18)99999}36\\\end{array}
Use the 7^{th} digit 6 from dividend 7964316
\begin{array}{l}\phantom{18)}0442462\phantom{14}\\18\overline{)7964316}\\\phantom{18)}\underline{\phantom{}72\phantom{99999}}\\\phantom{18)9}76\\\phantom{18)}\underline{\phantom{9}72\phantom{9999}}\\\phantom{18)99}44\\\phantom{18)}\underline{\phantom{99}36\phantom{999}}\\\phantom{18)999}83\\\phantom{18)}\underline{\phantom{999}72\phantom{99}}\\\phantom{18)999}111\\\phantom{18)}\underline{\phantom{999}108\phantom{9}}\\\phantom{18)99999}36\\\phantom{18)}\underline{\phantom{99999}36\phantom{}}\\\phantom{18)9999999}0\\\end{array}
Find closest multiple of 18 to 36. We see that 2 \times 18 = 36 is the nearest. Now subtract 36 from 36 to get reminder 0. Add 2 to quotient.
\text{Quotient: }442462 \text{Reminder: }0
Since 0 is less than 18, stop the division. The reminder is 0. The topmost line 0442462 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 442462.
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}