Evaluate
31
Factor
31
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\begin{array}{l}\phantom{15)}\phantom{1}\\15\overline{)465}\\\end{array}
Use the 1^{st} digit 4 from dividend 465
\begin{array}{l}\phantom{15)}0\phantom{2}\\15\overline{)465}\\\end{array}
Since 4 is less than 15, use the next digit 6 from dividend 465 and add 0 to the quotient
\begin{array}{l}\phantom{15)}0\phantom{3}\\15\overline{)465}\\\end{array}
Use the 2^{nd} digit 6 from dividend 465
\begin{array}{l}\phantom{15)}03\phantom{4}\\15\overline{)465}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}1\\\end{array}
Find closest multiple of 15 to 46. We see that 3 \times 15 = 45 is the nearest. Now subtract 45 from 46 to get reminder 1. Add 3 to quotient.
\begin{array}{l}\phantom{15)}03\phantom{5}\\15\overline{)465}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}15\\\end{array}
Use the 3^{rd} digit 5 from dividend 465
\begin{array}{l}\phantom{15)}031\phantom{6}\\15\overline{)465}\\\phantom{15)}\underline{\phantom{}45\phantom{9}}\\\phantom{15)9}15\\\phantom{15)}\underline{\phantom{9}15\phantom{}}\\\phantom{15)999}0\\\end{array}
Find closest multiple of 15 to 15. We see that 1 \times 15 = 15 is the nearest. Now subtract 15 from 15 to get reminder 0. Add 1 to quotient.
\text{Quotient: }31 \text{Reminder: }0
Since 0 is less than 15, stop the division. The reminder is 0. The topmost line 031 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 31.
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}