Question

prove that 33! is divisible by 2 raised to power 15 .what is the largest integer n such that 33! is divisible by 2 raised to power (n) ....???.........plz explain in detail

Answer 1

33! contains product of 1 through 33 , therefore 16 even numbers . Therefore , it must be divisible by 2^15 .Now , 33! contains 2x1 , 2x2 , ....2x16 as even terms  . Out of these there are 2,2^2,2^3 ,2^4therefore total 2's in 33! = 16+4=20therefore 33! is divisible by 2^n for a maximum value of n=20