Evaluate
315
Factor
3^{2}\times 5\times 7
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\begin{array}{l}\phantom{78)}\phantom{1}\\78\overline{)24570}\\\end{array}
Use the 1^{st} digit 2 from dividend 24570
\begin{array}{l}\phantom{78)}0\phantom{2}\\78\overline{)24570}\\\end{array}
Since 2 is less than 78, use the next digit 4 from dividend 24570 and add 0 to the quotient
\begin{array}{l}\phantom{78)}0\phantom{3}\\78\overline{)24570}\\\end{array}
Use the 2^{nd} digit 4 from dividend 24570
\begin{array}{l}\phantom{78)}00\phantom{4}\\78\overline{)24570}\\\end{array}
Since 24 is less than 78, use the next digit 5 from dividend 24570 and add 0 to the quotient
\begin{array}{l}\phantom{78)}00\phantom{5}\\78\overline{)24570}\\\end{array}
Use the 3^{rd} digit 5 from dividend 24570
\begin{array}{l}\phantom{78)}003\phantom{6}\\78\overline{)24570}\\\phantom{78)}\underline{\phantom{}234\phantom{99}}\\\phantom{78)9}11\\\end{array}
Find closest multiple of 78 to 245. We see that 3 \times 78 = 234 is the nearest. Now subtract 234 from 245 to get reminder 11. Add 3 to quotient.
\begin{array}{l}\phantom{78)}003\phantom{7}\\78\overline{)24570}\\\phantom{78)}\underline{\phantom{}234\phantom{99}}\\\phantom{78)9}117\\\end{array}
Use the 4^{th} digit 7 from dividend 24570
\begin{array}{l}\phantom{78)}0031\phantom{8}\\78\overline{)24570}\\\phantom{78)}\underline{\phantom{}234\phantom{99}}\\\phantom{78)9}117\\\phantom{78)}\underline{\phantom{99}78\phantom{9}}\\\phantom{78)99}39\\\end{array}
Find closest multiple of 78 to 117. We see that 1 \times 78 = 78 is the nearest. Now subtract 78 from 117 to get reminder 39. Add 1 to quotient.
\begin{array}{l}\phantom{78)}0031\phantom{9}\\78\overline{)24570}\\\phantom{78)}\underline{\phantom{}234\phantom{99}}\\\phantom{78)9}117\\\phantom{78)}\underline{\phantom{99}78\phantom{9}}\\\phantom{78)99}390\\\end{array}
Use the 5^{th} digit 0 from dividend 24570
\begin{array}{l}\phantom{78)}00315\phantom{10}\\78\overline{)24570}\\\phantom{78)}\underline{\phantom{}234\phantom{99}}\\\phantom{78)9}117\\\phantom{78)}\underline{\phantom{99}78\phantom{9}}\\\phantom{78)99}390\\\phantom{78)}\underline{\phantom{99}390\phantom{}}\\\phantom{78)99999}0\\\end{array}
Find closest multiple of 78 to 390. We see that 5 \times 78 = 390 is the nearest. Now subtract 390 from 390 to get reminder 0. Add 5 to quotient.
\text{Quotient: }315 \text{Reminder: }0
Since 0 is less than 78, stop the division. The reminder is 0. The topmost line 00315 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 315.
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}