Permutations & Combinations
Legendre's Formula — Largest Power of 7 in 101!
nta_pyq_2026_jan
Grade 11
Question:
The largest $n\in\mathbb{N}$, for which $7^n$ divides $101!$, is:
Step-by-Step Solution
Key Concept: Use Legendre's formula: exponent of 7 in $101!=\left\lfloor\tfrac{101}{7}\right\rfloor+\left\lfloor\tfrac{101}{49}\right\rfloor+\left\lfloor\tfrac{101}{343}\right\rfloor+\cdots$
Largest $n=16$.
Correct Answer: 1