Evaluate
\frac{51675}{2}=25837.5
Factor
\frac{3 \cdot 5 ^ {2} \cdot 13 \cdot 53}{2} = 25837\frac{1}{2} = 25837.5
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\begin{array}{l}\phantom{32)}\phantom{1}\\32\overline{)826800}\\\end{array}
Use the 1^{st} digit 8 from dividend 826800
\begin{array}{l}\phantom{32)}0\phantom{2}\\32\overline{)826800}\\\end{array}
Since 8 is less than 32, use the next digit 2 from dividend 826800 and add 0 to the quotient
\begin{array}{l}\phantom{32)}0\phantom{3}\\32\overline{)826800}\\\end{array}
Use the 2^{nd} digit 2 from dividend 826800
\begin{array}{l}\phantom{32)}02\phantom{4}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}18\\\end{array}
Find closest multiple of 32 to 82. We see that 2 \times 32 = 64 is the nearest. Now subtract 64 from 82 to get reminder 18. Add 2 to quotient.
\begin{array}{l}\phantom{32)}02\phantom{5}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}186\\\end{array}
Use the 3^{rd} digit 6 from dividend 826800
\begin{array}{l}\phantom{32)}025\phantom{6}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}186\\\phantom{32)}\underline{\phantom{}160\phantom{999}}\\\phantom{32)9}26\\\end{array}
Find closest multiple of 32 to 186. We see that 5 \times 32 = 160 is the nearest. Now subtract 160 from 186 to get reminder 26. Add 5 to quotient.
\begin{array}{l}\phantom{32)}025\phantom{7}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}186\\\phantom{32)}\underline{\phantom{}160\phantom{999}}\\\phantom{32)9}268\\\end{array}
Use the 4^{th} digit 8 from dividend 826800
\begin{array}{l}\phantom{32)}0258\phantom{8}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}186\\\phantom{32)}\underline{\phantom{}160\phantom{999}}\\\phantom{32)9}268\\\phantom{32)}\underline{\phantom{9}256\phantom{99}}\\\phantom{32)99}12\\\end{array}
Find closest multiple of 32 to 268. We see that 8 \times 32 = 256 is the nearest. Now subtract 256 from 268 to get reminder 12. Add 8 to quotient.
\begin{array}{l}\phantom{32)}0258\phantom{9}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}186\\\phantom{32)}\underline{\phantom{}160\phantom{999}}\\\phantom{32)9}268\\\phantom{32)}\underline{\phantom{9}256\phantom{99}}\\\phantom{32)99}120\\\end{array}
Use the 5^{th} digit 0 from dividend 826800
\begin{array}{l}\phantom{32)}02583\phantom{10}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}186\\\phantom{32)}\underline{\phantom{}160\phantom{999}}\\\phantom{32)9}268\\\phantom{32)}\underline{\phantom{9}256\phantom{99}}\\\phantom{32)99}120\\\phantom{32)}\underline{\phantom{999}96\phantom{9}}\\\phantom{32)999}24\\\end{array}
Find closest multiple of 32 to 120. We see that 3 \times 32 = 96 is the nearest. Now subtract 96 from 120 to get reminder 24. Add 3 to quotient.
\begin{array}{l}\phantom{32)}02583\phantom{11}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}186\\\phantom{32)}\underline{\phantom{}160\phantom{999}}\\\phantom{32)9}268\\\phantom{32)}\underline{\phantom{9}256\phantom{99}}\\\phantom{32)99}120\\\phantom{32)}\underline{\phantom{999}96\phantom{9}}\\\phantom{32)999}240\\\end{array}
Use the 6^{th} digit 0 from dividend 826800
\begin{array}{l}\phantom{32)}025837\phantom{12}\\32\overline{)826800}\\\phantom{32)}\underline{\phantom{}64\phantom{9999}}\\\phantom{32)}186\\\phantom{32)}\underline{\phantom{}160\phantom{999}}\\\phantom{32)9}268\\\phantom{32)}\underline{\phantom{9}256\phantom{99}}\\\phantom{32)99}120\\\phantom{32)}\underline{\phantom{999}96\phantom{9}}\\\phantom{32)999}240\\\phantom{32)}\underline{\phantom{999}224\phantom{}}\\\phantom{32)9999}16\\\end{array}
Find closest multiple of 32 to 240. We see that 7 \times 32 = 224 is the nearest. Now subtract 224 from 240 to get reminder 16. Add 7 to quotient.
\text{Quotient: }25837 \text{Reminder: }16
Since 16 is less than 32, stop the division. The reminder is 16. The topmost line 025837 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 25837.
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}