Evaluate
15747
Factor
3\times 29\times 181
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\begin{array}{l}\phantom{120)}\phantom{1}\\120\overline{)1889640}\\\end{array}
Use the 1^{st} digit 1 from dividend 1889640
\begin{array}{l}\phantom{120)}0\phantom{2}\\120\overline{)1889640}\\\end{array}
Since 1 is less than 120, use the next digit 8 from dividend 1889640 and add 0 to the quotient
\begin{array}{l}\phantom{120)}0\phantom{3}\\120\overline{)1889640}\\\end{array}
Use the 2^{nd} digit 8 from dividend 1889640
\begin{array}{l}\phantom{120)}00\phantom{4}\\120\overline{)1889640}\\\end{array}
Since 18 is less than 120, use the next digit 8 from dividend 1889640 and add 0 to the quotient
\begin{array}{l}\phantom{120)}00\phantom{5}\\120\overline{)1889640}\\\end{array}
Use the 3^{rd} digit 8 from dividend 1889640
\begin{array}{l}\phantom{120)}001\phantom{6}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}68\\\end{array}
Find closest multiple of 120 to 188. We see that 1 \times 120 = 120 is the nearest. Now subtract 120 from 188 to get reminder 68. Add 1 to quotient.
\begin{array}{l}\phantom{120)}001\phantom{7}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}689\\\end{array}
Use the 4^{th} digit 9 from dividend 1889640
\begin{array}{l}\phantom{120)}0015\phantom{8}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}689\\\phantom{120)}\underline{\phantom{9}600\phantom{999}}\\\phantom{120)99}89\\\end{array}
Find closest multiple of 120 to 689. We see that 5 \times 120 = 600 is the nearest. Now subtract 600 from 689 to get reminder 89. Add 5 to quotient.
\begin{array}{l}\phantom{120)}0015\phantom{9}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}689\\\phantom{120)}\underline{\phantom{9}600\phantom{999}}\\\phantom{120)99}896\\\end{array}
Use the 5^{th} digit 6 from dividend 1889640
\begin{array}{l}\phantom{120)}00157\phantom{10}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}689\\\phantom{120)}\underline{\phantom{9}600\phantom{999}}\\\phantom{120)99}896\\\phantom{120)}\underline{\phantom{99}840\phantom{99}}\\\phantom{120)999}56\\\end{array}
Find closest multiple of 120 to 896. We see that 7 \times 120 = 840 is the nearest. Now subtract 840 from 896 to get reminder 56. Add 7 to quotient.
\begin{array}{l}\phantom{120)}00157\phantom{11}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}689\\\phantom{120)}\underline{\phantom{9}600\phantom{999}}\\\phantom{120)99}896\\\phantom{120)}\underline{\phantom{99}840\phantom{99}}\\\phantom{120)999}564\\\end{array}
Use the 6^{th} digit 4 from dividend 1889640
\begin{array}{l}\phantom{120)}001574\phantom{12}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}689\\\phantom{120)}\underline{\phantom{9}600\phantom{999}}\\\phantom{120)99}896\\\phantom{120)}\underline{\phantom{99}840\phantom{99}}\\\phantom{120)999}564\\\phantom{120)}\underline{\phantom{999}480\phantom{9}}\\\phantom{120)9999}84\\\end{array}
Find closest multiple of 120 to 564. We see that 4 \times 120 = 480 is the nearest. Now subtract 480 from 564 to get reminder 84. Add 4 to quotient.
\begin{array}{l}\phantom{120)}001574\phantom{13}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}689\\\phantom{120)}\underline{\phantom{9}600\phantom{999}}\\\phantom{120)99}896\\\phantom{120)}\underline{\phantom{99}840\phantom{99}}\\\phantom{120)999}564\\\phantom{120)}\underline{\phantom{999}480\phantom{9}}\\\phantom{120)9999}840\\\end{array}
Use the 7^{th} digit 0 from dividend 1889640
\begin{array}{l}\phantom{120)}0015747\phantom{14}\\120\overline{)1889640}\\\phantom{120)}\underline{\phantom{}120\phantom{9999}}\\\phantom{120)9}689\\\phantom{120)}\underline{\phantom{9}600\phantom{999}}\\\phantom{120)99}896\\\phantom{120)}\underline{\phantom{99}840\phantom{99}}\\\phantom{120)999}564\\\phantom{120)}\underline{\phantom{999}480\phantom{9}}\\\phantom{120)9999}840\\\phantom{120)}\underline{\phantom{9999}840\phantom{}}\\\phantom{120)9999999}0\\\end{array}
Find closest multiple of 120 to 840. We see that 7 \times 120 = 840 is the nearest. Now subtract 840 from 840 to get reminder 0. Add 7 to quotient.
\text{Quotient: }15747 \text{Reminder: }0
Since 0 is less than 120, stop the division. The reminder is 0. The topmost line 0015747 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 15747.
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}