If 2^z is a factor of 26!, which of the following could be the value of z?
I. 22
II. 23
III. 24  Choose the correct choice from the following choices:
A) I ​ only B) II only C) I​ and II D) I, II, and III E) None
26! contains all numbers from 1 to 26. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.   Multiples of 2 = 13   Multiples of 4 = 6   Multiples of 8 = 3   Multiples of 16 = 1   Total count = 23   The answer is I​ and II.
<result>C</result>
If 2^z is a factor of 26!, which of the following could be the value of z?
I. 22
II. 23
III. 24