Evaluate
4224
Factor
2^{7}\times 3\times 11
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\begin{array}{l}\phantom{78)}\phantom{1}\\78\overline{)329472}\\\end{array}
Use the 1^{st} digit 3 from dividend 329472
\begin{array}{l}\phantom{78)}0\phantom{2}\\78\overline{)329472}\\\end{array}
Since 3 is less than 78, use the next digit 2 from dividend 329472 and add 0 to the quotient
\begin{array}{l}\phantom{78)}0\phantom{3}\\78\overline{)329472}\\\end{array}
Use the 2^{nd} digit 2 from dividend 329472
\begin{array}{l}\phantom{78)}00\phantom{4}\\78\overline{)329472}\\\end{array}
Since 32 is less than 78, use the next digit 9 from dividend 329472 and add 0 to the quotient
\begin{array}{l}\phantom{78)}00\phantom{5}\\78\overline{)329472}\\\end{array}
Use the 3^{rd} digit 9 from dividend 329472
\begin{array}{l}\phantom{78)}004\phantom{6}\\78\overline{)329472}\\\phantom{78)}\underline{\phantom{}312\phantom{999}}\\\phantom{78)9}17\\\end{array}
Find closest multiple of 78 to 329. We see that 4 \times 78 = 312 is the nearest. Now subtract 312 from 329 to get reminder 17. Add 4 to quotient.
\begin{array}{l}\phantom{78)}004\phantom{7}\\78\overline{)329472}\\\phantom{78)}\underline{\phantom{}312\phantom{999}}\\\phantom{78)9}174\\\end{array}
Use the 4^{th} digit 4 from dividend 329472
\begin{array}{l}\phantom{78)}0042\phantom{8}\\78\overline{)329472}\\\phantom{78)}\underline{\phantom{}312\phantom{999}}\\\phantom{78)9}174\\\phantom{78)}\underline{\phantom{9}156\phantom{99}}\\\phantom{78)99}18\\\end{array}
Find closest multiple of 78 to 174. We see that 2 \times 78 = 156 is the nearest. Now subtract 156 from 174 to get reminder 18. Add 2 to quotient.
\begin{array}{l}\phantom{78)}0042\phantom{9}\\78\overline{)329472}\\\phantom{78)}\underline{\phantom{}312\phantom{999}}\\\phantom{78)9}174\\\phantom{78)}\underline{\phantom{9}156\phantom{99}}\\\phantom{78)99}187\\\end{array}
Use the 5^{th} digit 7 from dividend 329472
\begin{array}{l}\phantom{78)}00422\phantom{10}\\78\overline{)329472}\\\phantom{78)}\underline{\phantom{}312\phantom{999}}\\\phantom{78)9}174\\\phantom{78)}\underline{\phantom{9}156\phantom{99}}\\\phantom{78)99}187\\\phantom{78)}\underline{\phantom{99}156\phantom{9}}\\\phantom{78)999}31\\\end{array}
Find closest multiple of 78 to 187. We see that 2 \times 78 = 156 is the nearest. Now subtract 156 from 187 to get reminder 31. Add 2 to quotient.
\begin{array}{l}\phantom{78)}00422\phantom{11}\\78\overline{)329472}\\\phantom{78)}\underline{\phantom{}312\phantom{999}}\\\phantom{78)9}174\\\phantom{78)}\underline{\phantom{9}156\phantom{99}}\\\phantom{78)99}187\\\phantom{78)}\underline{\phantom{99}156\phantom{9}}\\\phantom{78)999}312\\\end{array}
Use the 6^{th} digit 2 from dividend 329472
\begin{array}{l}\phantom{78)}004224\phantom{12}\\78\overline{)329472}\\\phantom{78)}\underline{\phantom{}312\phantom{999}}\\\phantom{78)9}174\\\phantom{78)}\underline{\phantom{9}156\phantom{99}}\\\phantom{78)99}187\\\phantom{78)}\underline{\phantom{99}156\phantom{9}}\\\phantom{78)999}312\\\phantom{78)}\underline{\phantom{999}312\phantom{}}\\\phantom{78)999999}0\\\end{array}
Find closest multiple of 78 to 312. We see that 4 \times 78 = 312 is the nearest. Now subtract 312 from 312 to get reminder 0. Add 4 to quotient.
\text{Quotient: }4224 \text{Reminder: }0
Since 0 is less than 78, stop the division. The reminder is 0. The topmost line 004224 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 4224.
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}