Evaluate
\frac{1500000}{23}\approx 65217.391304348
Factor
\frac{2 ^ {5} \cdot 3 \cdot 5 ^ {6}}{23} = 65217\frac{9}{23} = 65217.391304347824
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\begin{array}{l}\phantom{23)}\phantom{1}\\23\overline{)1500000}\\\end{array}
Use the 1^{st} digit 1 from dividend 1500000
\begin{array}{l}\phantom{23)}0\phantom{2}\\23\overline{)1500000}\\\end{array}
Since 1 is less than 23, use the next digit 5 from dividend 1500000 and add 0 to the quotient
\begin{array}{l}\phantom{23)}0\phantom{3}\\23\overline{)1500000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 1500000
\begin{array}{l}\phantom{23)}00\phantom{4}\\23\overline{)1500000}\\\end{array}
Since 15 is less than 23, use the next digit 0 from dividend 1500000 and add 0 to the quotient
\begin{array}{l}\phantom{23)}00\phantom{5}\\23\overline{)1500000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 1500000
\begin{array}{l}\phantom{23)}006\phantom{6}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}12\\\end{array}
Find closest multiple of 23 to 150. We see that 6 \times 23 = 138 is the nearest. Now subtract 138 from 150 to get reminder 12. Add 6 to quotient.
\begin{array}{l}\phantom{23)}006\phantom{7}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}120\\\end{array}
Use the 4^{th} digit 0 from dividend 1500000
\begin{array}{l}\phantom{23)}0065\phantom{8}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}120\\\phantom{23)}\underline{\phantom{9}115\phantom{999}}\\\phantom{23)999}5\\\end{array}
Find closest multiple of 23 to 120. We see that 5 \times 23 = 115 is the nearest. Now subtract 115 from 120 to get reminder 5. Add 5 to quotient.
\begin{array}{l}\phantom{23)}0065\phantom{9}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}120\\\phantom{23)}\underline{\phantom{9}115\phantom{999}}\\\phantom{23)999}50\\\end{array}
Use the 5^{th} digit 0 from dividend 1500000
\begin{array}{l}\phantom{23)}00652\phantom{10}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}120\\\phantom{23)}\underline{\phantom{9}115\phantom{999}}\\\phantom{23)999}50\\\phantom{23)}\underline{\phantom{999}46\phantom{99}}\\\phantom{23)9999}4\\\end{array}
Find closest multiple of 23 to 50. We see that 2 \times 23 = 46 is the nearest. Now subtract 46 from 50 to get reminder 4. Add 2 to quotient.
\begin{array}{l}\phantom{23)}00652\phantom{11}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}120\\\phantom{23)}\underline{\phantom{9}115\phantom{999}}\\\phantom{23)999}50\\\phantom{23)}\underline{\phantom{999}46\phantom{99}}\\\phantom{23)9999}40\\\end{array}
Use the 6^{th} digit 0 from dividend 1500000
\begin{array}{l}\phantom{23)}006521\phantom{12}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}120\\\phantom{23)}\underline{\phantom{9}115\phantom{999}}\\\phantom{23)999}50\\\phantom{23)}\underline{\phantom{999}46\phantom{99}}\\\phantom{23)9999}40\\\phantom{23)}\underline{\phantom{9999}23\phantom{9}}\\\phantom{23)9999}17\\\end{array}
Find closest multiple of 23 to 40. We see that 1 \times 23 = 23 is the nearest. Now subtract 23 from 40 to get reminder 17. Add 1 to quotient.
\begin{array}{l}\phantom{23)}006521\phantom{13}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}120\\\phantom{23)}\underline{\phantom{9}115\phantom{999}}\\\phantom{23)999}50\\\phantom{23)}\underline{\phantom{999}46\phantom{99}}\\\phantom{23)9999}40\\\phantom{23)}\underline{\phantom{9999}23\phantom{9}}\\\phantom{23)9999}170\\\end{array}
Use the 7^{th} digit 0 from dividend 1500000
\begin{array}{l}\phantom{23)}0065217\phantom{14}\\23\overline{)1500000}\\\phantom{23)}\underline{\phantom{}138\phantom{9999}}\\\phantom{23)9}120\\\phantom{23)}\underline{\phantom{9}115\phantom{999}}\\\phantom{23)999}50\\\phantom{23)}\underline{\phantom{999}46\phantom{99}}\\\phantom{23)9999}40\\\phantom{23)}\underline{\phantom{9999}23\phantom{9}}\\\phantom{23)9999}170\\\phantom{23)}\underline{\phantom{9999}161\phantom{}}\\\phantom{23)999999}9\\\end{array}
Find closest multiple of 23 to 170. We see that 7 \times 23 = 161 is the nearest. Now subtract 161 from 170 to get reminder 9. Add 7 to quotient.
\text{Quotient: }65217 \text{Reminder: }9
Since 9 is less than 23, stop the division. The reminder is 9. The topmost line 0065217 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 65217.
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}