Evaluate
123456789
Factor
3^{2}\times 3607\times 3803
Share
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\begin{array}{l}\phantom{10)}\phantom{1}\\10\overline{)1234567890}\\\end{array}
Use the 1^{st} digit 1 from dividend 1234567890
\begin{array}{l}\phantom{10)}0\phantom{2}\\10\overline{)1234567890}\\\end{array}
Since 1 is less than 10, use the next digit 2 from dividend 1234567890 and add 0 to the quotient
\begin{array}{l}\phantom{10)}0\phantom{3}\\10\overline{)1234567890}\\\end{array}
Use the 2^{nd} digit 2 from dividend 1234567890
\begin{array}{l}\phantom{10)}01\phantom{4}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}2\\\end{array}
Find closest multiple of 10 to 12. We see that 1 \times 10 = 10 is the nearest. Now subtract 10 from 12 to get reminder 2. Add 1 to quotient.
\begin{array}{l}\phantom{10)}01\phantom{5}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\end{array}
Use the 3^{rd} digit 3 from dividend 1234567890
\begin{array}{l}\phantom{10)}012\phantom{6}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}3\\\end{array}
Find closest multiple of 10 to 23. We see that 2 \times 10 = 20 is the nearest. Now subtract 20 from 23 to get reminder 3. Add 2 to quotient.
\begin{array}{l}\phantom{10)}012\phantom{7}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\end{array}
Use the 4^{th} digit 4 from dividend 1234567890
\begin{array}{l}\phantom{10)}0123\phantom{8}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}4\\\end{array}
Find closest multiple of 10 to 34. We see that 3 \times 10 = 30 is the nearest. Now subtract 30 from 34 to get reminder 4. Add 3 to quotient.
\begin{array}{l}\phantom{10)}0123\phantom{9}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\end{array}
Use the 5^{th} digit 5 from dividend 1234567890
\begin{array}{l}\phantom{10)}01234\phantom{10}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}5\\\end{array}
Find closest multiple of 10 to 45. We see that 4 \times 10 = 40 is the nearest. Now subtract 40 from 45 to get reminder 5. Add 4 to quotient.
\begin{array}{l}\phantom{10)}01234\phantom{11}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\end{array}
Use the 6^{th} digit 6 from dividend 1234567890
\begin{array}{l}\phantom{10)}012345\phantom{12}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}6\\\end{array}
Find closest multiple of 10 to 56. We see that 5 \times 10 = 50 is the nearest. Now subtract 50 from 56 to get reminder 6. Add 5 to quotient.
\begin{array}{l}\phantom{10)}012345\phantom{13}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}67\\\end{array}
Use the 7^{th} digit 7 from dividend 1234567890
\begin{array}{l}\phantom{10)}0123456\phantom{14}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}67\\\phantom{10)}\underline{\phantom{99999}60\phantom{999}}\\\phantom{10)999999}7\\\end{array}
Find closest multiple of 10 to 67. We see that 6 \times 10 = 60 is the nearest. Now subtract 60 from 67 to get reminder 7. Add 6 to quotient.
\begin{array}{l}\phantom{10)}0123456\phantom{15}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}67\\\phantom{10)}\underline{\phantom{99999}60\phantom{999}}\\\phantom{10)999999}78\\\end{array}
Use the 8^{th} digit 8 from dividend 1234567890
\begin{array}{l}\phantom{10)}01234567\phantom{16}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}67\\\phantom{10)}\underline{\phantom{99999}60\phantom{999}}\\\phantom{10)999999}78\\\phantom{10)}\underline{\phantom{999999}70\phantom{99}}\\\phantom{10)9999999}8\\\end{array}
Find closest multiple of 10 to 78. We see that 7 \times 10 = 70 is the nearest. Now subtract 70 from 78 to get reminder 8. Add 7 to quotient.
\begin{array}{l}\phantom{10)}01234567\phantom{17}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}67\\\phantom{10)}\underline{\phantom{99999}60\phantom{999}}\\\phantom{10)999999}78\\\phantom{10)}\underline{\phantom{999999}70\phantom{99}}\\\phantom{10)9999999}89\\\end{array}
Use the 9^{th} digit 9 from dividend 1234567890
\begin{array}{l}\phantom{10)}012345678\phantom{18}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}67\\\phantom{10)}\underline{\phantom{99999}60\phantom{999}}\\\phantom{10)999999}78\\\phantom{10)}\underline{\phantom{999999}70\phantom{99}}\\\phantom{10)9999999}89\\\phantom{10)}\underline{\phantom{9999999}80\phantom{9}}\\\phantom{10)99999999}9\\\end{array}
Find closest multiple of 10 to 89. We see that 8 \times 10 = 80 is the nearest. Now subtract 80 from 89 to get reminder 9. Add 8 to quotient.
\begin{array}{l}\phantom{10)}012345678\phantom{19}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}67\\\phantom{10)}\underline{\phantom{99999}60\phantom{999}}\\\phantom{10)999999}78\\\phantom{10)}\underline{\phantom{999999}70\phantom{99}}\\\phantom{10)9999999}89\\\phantom{10)}\underline{\phantom{9999999}80\phantom{9}}\\\phantom{10)99999999}90\\\end{array}
Use the 10^{th} digit 0 from dividend 1234567890
\begin{array}{l}\phantom{10)}0123456789\phantom{20}\\10\overline{)1234567890}\\\phantom{10)}\underline{\phantom{}10\phantom{99999999}}\\\phantom{10)9}23\\\phantom{10)}\underline{\phantom{9}20\phantom{9999999}}\\\phantom{10)99}34\\\phantom{10)}\underline{\phantom{99}30\phantom{999999}}\\\phantom{10)999}45\\\phantom{10)}\underline{\phantom{999}40\phantom{99999}}\\\phantom{10)9999}56\\\phantom{10)}\underline{\phantom{9999}50\phantom{9999}}\\\phantom{10)99999}67\\\phantom{10)}\underline{\phantom{99999}60\phantom{999}}\\\phantom{10)999999}78\\\phantom{10)}\underline{\phantom{999999}70\phantom{99}}\\\phantom{10)9999999}89\\\phantom{10)}\underline{\phantom{9999999}80\phantom{9}}\\\phantom{10)99999999}90\\\phantom{10)}\underline{\phantom{99999999}90\phantom{}}\\\phantom{10)9999999999}0\\\end{array}
Find closest multiple of 10 to 90. We see that 9 \times 10 = 90 is the nearest. Now subtract 90 from 90 to get reminder 0. Add 9 to quotient.
\text{Quotient: }123456789 \text{Reminder: }0
Since 0 is less than 10, stop the division. The reminder is 0. The topmost line 0123456789 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 123456789.
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}