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The largest $\mathrm{n} \in \mathrm{N}$, for which $7^{\mathrm{n}}$ divides 101!, is
[JEE MAIN 21 Jan 2026 S II]
(1) 16
(2) 18
(3) 15
(4) 19Solution
Exponent of $7=\left[\frac{101}{7}\right]+\left[\frac{101}{49}\right]+\left[\frac{101}{49 \times 7}\right]+\cdots$
\[ =14+2+0=16 \]$101!=7^{16}(\lambda)$ Answer(1)
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