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please answer it as fast as you can and it is of mathematics

please answer it as fast as you can and it is of mathematics
 

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Grade:11

1 Answers

jagdish singh singh
173 Points
7 years ago
\hspace{-0.70 cm}$exponent of prime no. $p$ in $n!$ is $E_{p}(n!)=\bigg\lfloor \frac{n}{p} \bigg\rfloor +\bigg\lfloor \frac{n}{p^2} \bigg\rfloor +\bigg\lfloor \frac{n}{p^3} \bigg\rfloor +\cdots$\\\\\\ Where $\lfloor x \rfloor $ represent greatest integer function.\\\\\\ So $E_{17}(2050!) = \bigg\lfloor \frac{2015}{17}\bigg\rfloor+\bigg\lfloor \frac{2015}{17^2}\bigg\rfloor+\bigg\lfloor \frac{2015}{17^3}\bigg\rfloor+\bigg\lfloor \frac{2015}{17^4}\bigg\rfloor+\cdots$\\\\\\ So we get $E_{17}(2015) = 120+7+0+0+0\cdots =127$

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