Permutations & Combinations
Legendre's Formula — Largest n for 40ⁿ | 60!
nta_pyq_2026_jan
Grade None
Question:
The largest value of $n$, for which $40^n$ divides $60!$, is
Step-by-Step Solution
Key Concept: $40^n=2^{3n}\times5^n$. Power of 5 in $60!=12+2=14$. Power of 2 in $60!=30+15+7+3+1=56$. Need $3n\leq56$ and $n\leq14$.
Largest $n=14$.
Correct Answer: 3