JEE Main 2026 (Online) 24th January Evening ShiftQuestion 1
The largest value of $n$, for which $40^n$ divides $60!$, is :
Permutation and Combination
Solution
$40^n=2^{3n}5^n$. In $60!$: exponent of $5$ is $12+2=14$, exponent of $2$ is $56$ (so $3n\le56$). Hence $n\le\min(18,14)=14$.