The largest prime number among the given options is 23.

Explanation:
To identify the largest prime number among the given options, we need to understand what a prime number is. A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.

Given options:
a) 27
b) 23
c) 33
d) 39

Now, let's analyze each option:

a) 27:
To determine if 27 is a prime number, we need to check if it has any divisors other than 1 and itself. In this case, 27 can be divided evenly by 3, 9, and 27. Since it has divisors other than 1 and itself, 27 is not a prime number.

b) 23:
To determine if 23 is a prime number, we need to check if it has any divisors other than 1 and itself. In this case, 23 cannot be divided evenly by any other positive integer. Therefore, 23 is a prime number.

c) 33:
To determine if 33 is a prime number, we need to check if it has any divisors other than 1 and itself. In this case, 33 can be divided evenly by 3, 11, and 33. Since it has divisors other than 1 and itself, 33 is not a prime number.

d) 39:
To determine if 39 is a prime number, we need to check if it has any divisors other than 1 and itself. In this case, 39 can be divided evenly by 3, 13, and 39. Since it has divisors other than 1 and itself, 39 is not a prime number.

Therefore, among the given options, 23 is the largest prime number.

B