The largest natural number $n$ such that $3^{n}$ divides $66 !$ is ___________.
Answer (integer)
31
Solution
We have,
<br/><br/>$$
\begin{aligned}
& {\left[\frac{66}{3}\right]=22} \\\\
& {\left[\frac{66}{3^2}\right]=7} \\\\
& {\left[\frac{66}{3^3}\right]=2}
\end{aligned}
$$
<br/><br/>Highest powers of 3 is greater than 66. So, their g.i.f. is always 0.
<br/><br/>$\therefore$ Required natural number $=22+7+2=31$
About this question
Subject: Mathematics · Chapter: Binomial Theorem · Topic: Binomial Expansion
This question is part of PrepWiser's free JEE Main question bank. 193 more solved questions on Binomial Theorem are available — start with the harder ones if your accuracy is >70%.