If 2^z is a factor of 25!, which of the following could be the value of z?
If 2^z is a factor of 25!, which of the following could be the value of z?
I. 22
II. 23
III. 24
Answer/Solution
I only
Steps/Work
25! contains all numbers from 1 to 25. 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 = 12
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 22
A is the answer.
Multiples of 2 = 12
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 22
A is the answer.