JEE Main 20252 AprilMorning Shift

JEE Main 2025 · 2 April · Morning Shift · Mathematics · Permutation and Combination

The largest n ∈ N such that 3^ n divides 50 ! is:

The largest

\mathrm{n} \in \mathrm{N}

such that

3^{\mathrm{n}}

divides 50 ! is:

Options

B. 22

2^\alpha \cdot 3^\beta \cdot 5^\gamma

\mathrm{B}=\left[\frac{50}{3}\right]+\left[\frac{50}{3^2}\right]+\left[\frac{50}{3^3}\right]+\left[\frac{50}{3^4}\right]

=16+5+1

=2

Maximum value of

n

is 22