Binomial Theorem
Largest Power of Prime Dividing a Factorial (Legendre's Formula)
nta_pyq_2023_apr
Grade 11
Question:
The largest natural number $n$ such that $3^n$ divides $66!$ is _______.
Step-by-Step Solution
Key Concept: Use Legendre's formula: the exponent of prime $p$ in $a!$ is $\sum_{k=1}^\infty\lfloor\frac{a}{p^k}\rfloor$.
$22+7+2+0=31$.
Correct Answer: 31