Evaluate
6721
Factor
11\times 13\times 47
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\begin{array}{l}\phantom{37)}\phantom{1}\\37\overline{)248677}\\\end{array}
Use the 1^{st} digit 2 from dividend 248677
\begin{array}{l}\phantom{37)}0\phantom{2}\\37\overline{)248677}\\\end{array}
Since 2 is less than 37, use the next digit 4 from dividend 248677 and add 0 to the quotient
\begin{array}{l}\phantom{37)}0\phantom{3}\\37\overline{)248677}\\\end{array}
Use the 2^{nd} digit 4 from dividend 248677
\begin{array}{l}\phantom{37)}00\phantom{4}\\37\overline{)248677}\\\end{array}
Since 24 is less than 37, use the next digit 8 from dividend 248677 and add 0 to the quotient
\begin{array}{l}\phantom{37)}00\phantom{5}\\37\overline{)248677}\\\end{array}
Use the 3^{rd} digit 8 from dividend 248677
\begin{array}{l}\phantom{37)}006\phantom{6}\\37\overline{)248677}\\\phantom{37)}\underline{\phantom{}222\phantom{999}}\\\phantom{37)9}26\\\end{array}
Find closest multiple of 37 to 248. We see that 6 \times 37 = 222 is the nearest. Now subtract 222 from 248 to get reminder 26. Add 6 to quotient.
\begin{array}{l}\phantom{37)}006\phantom{7}\\37\overline{)248677}\\\phantom{37)}\underline{\phantom{}222\phantom{999}}\\\phantom{37)9}266\\\end{array}
Use the 4^{th} digit 6 from dividend 248677
\begin{array}{l}\phantom{37)}0067\phantom{8}\\37\overline{)248677}\\\phantom{37)}\underline{\phantom{}222\phantom{999}}\\\phantom{37)9}266\\\phantom{37)}\underline{\phantom{9}259\phantom{99}}\\\phantom{37)999}7\\\end{array}
Find closest multiple of 37 to 266. We see that 7 \times 37 = 259 is the nearest. Now subtract 259 from 266 to get reminder 7. Add 7 to quotient.
\begin{array}{l}\phantom{37)}0067\phantom{9}\\37\overline{)248677}\\\phantom{37)}\underline{\phantom{}222\phantom{999}}\\\phantom{37)9}266\\\phantom{37)}\underline{\phantom{9}259\phantom{99}}\\\phantom{37)999}77\\\end{array}
Use the 5^{th} digit 7 from dividend 248677
\begin{array}{l}\phantom{37)}00672\phantom{10}\\37\overline{)248677}\\\phantom{37)}\underline{\phantom{}222\phantom{999}}\\\phantom{37)9}266\\\phantom{37)}\underline{\phantom{9}259\phantom{99}}\\\phantom{37)999}77\\\phantom{37)}\underline{\phantom{999}74\phantom{9}}\\\phantom{37)9999}3\\\end{array}
Find closest multiple of 37 to 77. We see that 2 \times 37 = 74 is the nearest. Now subtract 74 from 77 to get reminder 3. Add 2 to quotient.
\begin{array}{l}\phantom{37)}00672\phantom{11}\\37\overline{)248677}\\\phantom{37)}\underline{\phantom{}222\phantom{999}}\\\phantom{37)9}266\\\phantom{37)}\underline{\phantom{9}259\phantom{99}}\\\phantom{37)999}77\\\phantom{37)}\underline{\phantom{999}74\phantom{9}}\\\phantom{37)9999}37\\\end{array}
Use the 6^{th} digit 7 from dividend 248677
\begin{array}{l}\phantom{37)}006721\phantom{12}\\37\overline{)248677}\\\phantom{37)}\underline{\phantom{}222\phantom{999}}\\\phantom{37)9}266\\\phantom{37)}\underline{\phantom{9}259\phantom{99}}\\\phantom{37)999}77\\\phantom{37)}\underline{\phantom{999}74\phantom{9}}\\\phantom{37)9999}37\\\phantom{37)}\underline{\phantom{9999}37\phantom{}}\\\phantom{37)999999}0\\\end{array}
Find closest multiple of 37 to 37. We see that 1 \times 37 = 37 is the nearest. Now subtract 37 from 37 to get reminder 0. Add 1 to quotient.
\text{Quotient: }6721 \text{Reminder: }0
Since 0 is less than 37, stop the division. The reminder is 0. The topmost line 006721 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 6721.
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}