Let N=1!*2!*3!*4!…9!*10! .Let 2^k be the largest power of 2 that divides N . What is the value of k ?

1! contains no 2's

2! contains 1
3! contains 1
4! contains 3 , the 2 and 4=2x2 for a total of 3
5! contains 3
6! contains 4
7! contains 4
8! contains 7 , 3 more 2's from 8 = 2x2x2
9! contains 7
10! constains 8

for a total of 38 2's
for the largest factor of only 2's being 2^38
so k = 38

check my thinking