Evaluate
\frac{31436789}{15}\approx 2095785.933333333
Factor
\frac{31436789}{3 \cdot 5} = 2095785\frac{14}{15} = 2095785.9333333333
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)94310367}\\\end{array}
Use the 1^{st} digit 9 from dividend 94310367
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)94310367}\\\end{array}
Since 9 is less than 45, use the next digit 4 from dividend 94310367 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)94310367}\\\end{array}
Use the 2^{nd} digit 4 from dividend 94310367
\begin{array}{l}\phantom{45)}02\phantom{4}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}4\\\end{array}
Find closest multiple of 45 to 94. We see that 2 \times 45 = 90 is the nearest. Now subtract 90 from 94 to get reminder 4. Add 2 to quotient.
\begin{array}{l}\phantom{45)}02\phantom{5}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}43\\\end{array}
Use the 3^{rd} digit 3 from dividend 94310367
\begin{array}{l}\phantom{45)}020\phantom{6}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}43\\\end{array}
Since 43 is less than 45, use the next digit 1 from dividend 94310367 and add 0 to the quotient
\begin{array}{l}\phantom{45)}020\phantom{7}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\end{array}
Use the 4^{th} digit 1 from dividend 94310367
\begin{array}{l}\phantom{45)}0209\phantom{8}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}26\\\end{array}
Find closest multiple of 45 to 431. We see that 9 \times 45 = 405 is the nearest. Now subtract 405 from 431 to get reminder 26. Add 9 to quotient.
\begin{array}{l}\phantom{45)}0209\phantom{9}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}260\\\end{array}
Use the 5^{th} digit 0 from dividend 94310367
\begin{array}{l}\phantom{45)}02095\phantom{10}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}260\\\phantom{45)}\underline{\phantom{99}225\phantom{999}}\\\phantom{45)999}35\\\end{array}
Find closest multiple of 45 to 260. We see that 5 \times 45 = 225 is the nearest. Now subtract 225 from 260 to get reminder 35. Add 5 to quotient.
\begin{array}{l}\phantom{45)}02095\phantom{11}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}260\\\phantom{45)}\underline{\phantom{99}225\phantom{999}}\\\phantom{45)999}353\\\end{array}
Use the 6^{th} digit 3 from dividend 94310367
\begin{array}{l}\phantom{45)}020957\phantom{12}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}260\\\phantom{45)}\underline{\phantom{99}225\phantom{999}}\\\phantom{45)999}353\\\phantom{45)}\underline{\phantom{999}315\phantom{99}}\\\phantom{45)9999}38\\\end{array}
Find closest multiple of 45 to 353. We see that 7 \times 45 = 315 is the nearest. Now subtract 315 from 353 to get reminder 38. Add 7 to quotient.
\begin{array}{l}\phantom{45)}020957\phantom{13}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}260\\\phantom{45)}\underline{\phantom{99}225\phantom{999}}\\\phantom{45)999}353\\\phantom{45)}\underline{\phantom{999}315\phantom{99}}\\\phantom{45)9999}386\\\end{array}
Use the 7^{th} digit 6 from dividend 94310367
\begin{array}{l}\phantom{45)}0209578\phantom{14}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}260\\\phantom{45)}\underline{\phantom{99}225\phantom{999}}\\\phantom{45)999}353\\\phantom{45)}\underline{\phantom{999}315\phantom{99}}\\\phantom{45)9999}386\\\phantom{45)}\underline{\phantom{9999}360\phantom{9}}\\\phantom{45)99999}26\\\end{array}
Find closest multiple of 45 to 386. We see that 8 \times 45 = 360 is the nearest. Now subtract 360 from 386 to get reminder 26. Add 8 to quotient.
\begin{array}{l}\phantom{45)}0209578\phantom{15}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}260\\\phantom{45)}\underline{\phantom{99}225\phantom{999}}\\\phantom{45)999}353\\\phantom{45)}\underline{\phantom{999}315\phantom{99}}\\\phantom{45)9999}386\\\phantom{45)}\underline{\phantom{9999}360\phantom{9}}\\\phantom{45)99999}267\\\end{array}
Use the 8^{th} digit 7 from dividend 94310367
\begin{array}{l}\phantom{45)}02095785\phantom{16}\\45\overline{)94310367}\\\phantom{45)}\underline{\phantom{}90\phantom{999999}}\\\phantom{45)9}431\\\phantom{45)}\underline{\phantom{9}405\phantom{9999}}\\\phantom{45)99}260\\\phantom{45)}\underline{\phantom{99}225\phantom{999}}\\\phantom{45)999}353\\\phantom{45)}\underline{\phantom{999}315\phantom{99}}\\\phantom{45)9999}386\\\phantom{45)}\underline{\phantom{9999}360\phantom{9}}\\\phantom{45)99999}267\\\phantom{45)}\underline{\phantom{99999}225\phantom{}}\\\phantom{45)999999}42\\\end{array}
Find closest multiple of 45 to 267. We see that 5 \times 45 = 225 is the nearest. Now subtract 225 from 267 to get reminder 42. Add 5 to quotient.
\text{Quotient: }2095785 \text{Reminder: }42
Since 42 is less than 45, stop the division. The reminder is 42. The topmost line 02095785 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 2095785.
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}