Evaluate
13
Factor
13
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\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)325}\\\end{array}
Use the 1^{st} digit 3 from dividend 325
\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)325}\\\end{array}
Since 3 is less than 25, use the next digit 2 from dividend 325 and add 0 to the quotient
\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)325}\\\end{array}
Use the 2^{nd} digit 2 from dividend 325
\begin{array}{l}\phantom{25)}01\phantom{4}\\25\overline{)325}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}7\\\end{array}
Find closest multiple of 25 to 32. We see that 1 \times 25 = 25 is the nearest. Now subtract 25 from 32 to get reminder 7. Add 1 to quotient.
\begin{array}{l}\phantom{25)}01\phantom{5}\\25\overline{)325}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}75\\\end{array}
Use the 3^{rd} digit 5 from dividend 325
\begin{array}{l}\phantom{25)}013\phantom{6}\\25\overline{)325}\\\phantom{25)}\underline{\phantom{}25\phantom{9}}\\\phantom{25)9}75\\\phantom{25)}\underline{\phantom{9}75\phantom{}}\\\phantom{25)999}0\\\end{array}
Find closest multiple of 25 to 75. We see that 3 \times 25 = 75 is the nearest. Now subtract 75 from 75 to get reminder 0. Add 3 to quotient.
\text{Quotient: }13 \text{Reminder: }0
Since 0 is less than 25, stop the division. The reminder is 0. The topmost line 013 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 13.
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}