Evaluate
17562
Factor
2\times 3\times 2927
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\begin{array}{l}\phantom{45)}\phantom{1}\\45\overline{)790290}\\\end{array}
Use the 1^{st} digit 7 from dividend 790290
\begin{array}{l}\phantom{45)}0\phantom{2}\\45\overline{)790290}\\\end{array}
Since 7 is less than 45, use the next digit 9 from dividend 790290 and add 0 to the quotient
\begin{array}{l}\phantom{45)}0\phantom{3}\\45\overline{)790290}\\\end{array}
Use the 2^{nd} digit 9 from dividend 790290
\begin{array}{l}\phantom{45)}01\phantom{4}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}34\\\end{array}
Find closest multiple of 45 to 79. We see that 1 \times 45 = 45 is the nearest. Now subtract 45 from 79 to get reminder 34. Add 1 to quotient.
\begin{array}{l}\phantom{45)}01\phantom{5}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}340\\\end{array}
Use the 3^{rd} digit 0 from dividend 790290
\begin{array}{l}\phantom{45)}017\phantom{6}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}340\\\phantom{45)}\underline{\phantom{}315\phantom{999}}\\\phantom{45)9}25\\\end{array}
Find closest multiple of 45 to 340. We see that 7 \times 45 = 315 is the nearest. Now subtract 315 from 340 to get reminder 25. Add 7 to quotient.
\begin{array}{l}\phantom{45)}017\phantom{7}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}340\\\phantom{45)}\underline{\phantom{}315\phantom{999}}\\\phantom{45)9}252\\\end{array}
Use the 4^{th} digit 2 from dividend 790290
\begin{array}{l}\phantom{45)}0175\phantom{8}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}340\\\phantom{45)}\underline{\phantom{}315\phantom{999}}\\\phantom{45)9}252\\\phantom{45)}\underline{\phantom{9}225\phantom{99}}\\\phantom{45)99}27\\\end{array}
Find closest multiple of 45 to 252. We see that 5 \times 45 = 225 is the nearest. Now subtract 225 from 252 to get reminder 27. Add 5 to quotient.
\begin{array}{l}\phantom{45)}0175\phantom{9}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}340\\\phantom{45)}\underline{\phantom{}315\phantom{999}}\\\phantom{45)9}252\\\phantom{45)}\underline{\phantom{9}225\phantom{99}}\\\phantom{45)99}279\\\end{array}
Use the 5^{th} digit 9 from dividend 790290
\begin{array}{l}\phantom{45)}01756\phantom{10}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}340\\\phantom{45)}\underline{\phantom{}315\phantom{999}}\\\phantom{45)9}252\\\phantom{45)}\underline{\phantom{9}225\phantom{99}}\\\phantom{45)99}279\\\phantom{45)}\underline{\phantom{99}270\phantom{9}}\\\phantom{45)9999}9\\\end{array}
Find closest multiple of 45 to 279. We see that 6 \times 45 = 270 is the nearest. Now subtract 270 from 279 to get reminder 9. Add 6 to quotient.
\begin{array}{l}\phantom{45)}01756\phantom{11}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}340\\\phantom{45)}\underline{\phantom{}315\phantom{999}}\\\phantom{45)9}252\\\phantom{45)}\underline{\phantom{9}225\phantom{99}}\\\phantom{45)99}279\\\phantom{45)}\underline{\phantom{99}270\phantom{9}}\\\phantom{45)9999}90\\\end{array}
Use the 6^{th} digit 0 from dividend 790290
\begin{array}{l}\phantom{45)}017562\phantom{12}\\45\overline{)790290}\\\phantom{45)}\underline{\phantom{}45\phantom{9999}}\\\phantom{45)}340\\\phantom{45)}\underline{\phantom{}315\phantom{999}}\\\phantom{45)9}252\\\phantom{45)}\underline{\phantom{9}225\phantom{99}}\\\phantom{45)99}279\\\phantom{45)}\underline{\phantom{99}270\phantom{9}}\\\phantom{45)9999}90\\\phantom{45)}\underline{\phantom{9999}90\phantom{}}\\\phantom{45)999999}0\\\end{array}
Find closest multiple of 45 to 90. We see that 2 \times 45 = 90 is the nearest. Now subtract 90 from 90 to get reminder 0. Add 2 to quotient.
\text{Quotient: }17562 \text{Reminder: }0
Since 0 is less than 45, stop the division. The reminder is 0. The topmost line 017562 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 17562.
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}