The largest n in mathbb{N} such that 3^n divi | vedclass

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(B) To find the largest exponent $n$ such that $3^n$ divides $50!$,we use Legendre's Formula: $E_p(m!) = \sum_{k=1}^{\infty} \left[ \frac{m}{p^k} \rig

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$22$

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(B) To find the largest exponent $n$ such that $3^n$ divides $50!$,we use Legendre's Formula: $E_p(m!) = \sum_{k=1}^{\infty} \left[ \frac{m}{p^k} \right]$.Here,$m = 50$ and $p = 3$.$n = \left[ \frac{50}{3} \right] + \left[ \frac{50}{3^2} \right] + \left[ \frac{50}{3^3} \right] + \left[ \frac{50}{3^4} \right]$$n = \left[ \frac{50}{3} \right] + \left[ \frac{50}{9} \right] + \left[ \frac{50}{27} \right] + \left[ \frac{50}{81} \right]$$n = 16 + 5 + 1 + 0$$n = 22$.Thus,the largest $n$ is $22$.

The largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is:

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