The number of zeros at the end of 100! is | vedclass

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(D) To find the number of zeros at the end of $100!$, we need to calculate the exponent of the highest power of $5$ that divides $100!$, denoted as $E

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(D) To find the number of zeros at the end of $100!$, we need to calculate the exponent of the highest power of $5$ that divides $100!$, denoted as $E_5(100!)$.Using Legendre's Formula: $E_p(n!) = \sum_{k=1}^{\infty} \left[ \frac{n}{p^k} \right]$.For $n = 100$ and $p = 5$:$E_5(100!) = \left[ \frac{100}{5} \right] + \left[ \frac{100}{25} \right] + \left[ \frac{100}{125} \right]$$E_5(100!) = 20 + 4 + 0 = 24$.Therefore, there are $24$ zeros at the end of $100!$.

The number of zeros at the end of $100!$ is

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