Evaluate
1346
Factor
2\times 673
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)60570}\\\end{array}
Use the 1^{st} digit 6 from dividend 60570
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)60570}\\\end{array}
Since 6 is less than 45, use the next digit 0 from dividend 60570 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)60570}\\\end{array}
Use the 2^{nd} digit 0 from dividend 60570
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)60570}\\\phantom{45)}\underline{\phantom{}45\phantom{999}}\\\phantom{45)}15\\\end{array}
Find closest multiple of 45 to 60. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 60 to get reminder 15. Add 1 to quotient.
\begin{array}{l}\phantom{45)}01\phantom{5}\\45\overline{)60570}\\\phantom{45)}\underline{\phantom{}45\phantom{999}}\\\phantom{45)}155\\\end{array}
Use the 3^{rd} digit 5 from dividend 60570
\begin{array}{l}\phantom{45)}013\phantom{6}\\45\overline{)60570}\\\phantom{45)}\underline{\phantom{}45\phantom{999}}\\\phantom{45)}155\\\phantom{45)}\underline{\phantom{}135\phantom{99}}\\\phantom{45)9}20\\\end{array}
Find closest multiple of 45 to 155. We see that 3 \times 45 = 135 is the nearest. Now subtract 135 from 155 to get reminder 20. Add 3 to quotient.
\begin{array}{l}\phantom{45)}013\phantom{7}\\45\overline{)60570}\\\phantom{45)}\underline{\phantom{}45\phantom{999}}\\\phantom{45)}155\\\phantom{45)}\underline{\phantom{}135\phantom{99}}\\\phantom{45)9}207\\\end{array}
Use the 4^{th} digit 7 from dividend 60570
\begin{array}{l}\phantom{45)}0134\phantom{8}\\45\overline{)60570}\\\phantom{45)}\underline{\phantom{}45\phantom{999}}\\\phantom{45)}155\\\phantom{45)}\underline{\phantom{}135\phantom{99}}\\\phantom{45)9}207\\\phantom{45)}\underline{\phantom{9}180\phantom{9}}\\\phantom{45)99}27\\\end{array}
Find closest multiple of 45 to 207. We see that 4 \times 45 = 180 is the nearest. Now subtract 180 from 207 to get reminder 27. Add 4 to quotient.
\begin{array}{l}\phantom{45)}0134\phantom{9}\\45\overline{)60570}\\\phantom{45)}\underline{\phantom{}45\phantom{999}}\\\phantom{45)}155\\\phantom{45)}\underline{\phantom{}135\phantom{99}}\\\phantom{45)9}207\\\phantom{45)}\underline{\phantom{9}180\phantom{9}}\\\phantom{45)99}270\\\end{array}
Use the 5^{th} digit 0 from dividend 60570
\begin{array}{l}\phantom{45)}01346\phantom{10}\\45\overline{)60570}\\\phantom{45)}\underline{\phantom{}45\phantom{999}}\\\phantom{45)}155\\\phantom{45)}\underline{\phantom{}135\phantom{99}}\\\phantom{45)9}207\\\phantom{45)}\underline{\phantom{9}180\phantom{9}}\\\phantom{45)99}270\\\phantom{45)}\underline{\phantom{99}270\phantom{}}\\\phantom{45)99999}0\\\end{array}
Find closest multiple of 45 to 270. We see that 6 \times 45 = 270 is the nearest. Now subtract 270 from 270 to get reminder 0. Add 6 to quotient.
\text{Quotient: }1346 \text{Reminder: }0
Since 0 is less than 45, stop the division. The reminder is 0. The topmost line 01346 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1346.
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}