Question

Maximum value n such that (66)! is divisible by 3n

Answer 1

The correct answer is : 31

$\because$ 3 sis prime number,

$[\frac{66}{3}]+[\frac{66}{3^2}]+[\frac{66}{3^3}]+[\frac{66}{3^4}]+........$

$\Rightarrow$ 22+7+2+0+………

= 31

$(66)!=(3)^{31}........$

maximum value of n=31