The largest integer n such that 33! is divisible by 2n is

In terms of prime factors 33! can be written as 2a ⋅ 3b 5c ⋅ 7d …Now, E2 (33!)=332+3322+3323+3324+3325=16+8+4+2+1=31.Hence, the exponent of 2 in 33! is 31.∴ Largest value of n is 31.