Verified Solution • 2025–26 Session moderate

QJEEM23Ma9180: JEE Main 2023 Mathematics - Class 11 JEEM23Ma9180 Solution: The largest natural number such that divides is ___________.

The largest natural number nn such that 3n3^{n} divides 66!66 ! is ___________.

Step-by-Step Verified Solution

We have,

amp;[663]=22amp;[6632]=7amp;[6633]=2\begin{aligned}& {\left[\frac{66}{3}\right]=22} \\\\& {\left[\frac{66}{3^2}\right]=7} \\\\& {\left[\frac{66}{3^3}\right]=2}\end{aligned}

Highest powers of 3 is greater than 66. So, their g.i.f. is always 0.

∴\therefore Required natural number =22+7+2=31=22+7+2=31

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring