Question 41 — JEE Main 21 Jan 2026 S Ii

Question

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) 19

Solution

Exponent of $7=\left[\frac{101}{7}\right]+\left[\frac{101}{49}\right]+\left[\frac{101}{49 \times 7}\right]+\cdots$

$101!=7^{16}(\lambda)$ Answer(1)