JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Permutations and Combinations

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The largest , for which divides 101!, is:
  1. (A)16✓ Correct
  2. (B)18
  3. (C)15
  4. (D)19

Answer: (A)

Solution

The exponent of prime p in n! is given by Legendre's formula:


For and :



Therefore, the largest n for which divides 101! is 16.

JEE Main · 2026 · 21 Jan 2026 · Shift 2 · Single correct option

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