Given:
BB = 169

To find:
The values of a, c, and d.

Solution:

We are given that BB = 169. Let's break down the value of BB into its prime factors to find the values of a, c, and d.

Prime Factorization of 169:
169 can be written as the square of a prime number, which is 13. Therefore, the prime factorization of 169 is 13 * 13.

Since we are looking for three values (a, c, and d), we'll assume that the prime factorization of BB can be expressed as the product of three prime numbers, which are a, c, and d.

Prime Factorization of BB:
BB = a * c * d

Dividing BB by 13:
169 ÷ 13 = 13
After dividing BB by 13, we are left with another 13. This means that one of the values (a, c, or d) must equal 13.

By substitution:
BB = a * 13 * d

Since 13 is a prime number, it cannot be further factorized. So, we need to find the remaining two values, a and d, such that their product equals 169 ÷ 13 = 13.

Factors of 13:
The factors of 13 are 1 and 13 itself.

Therefore, the possible combinations for a and d are:
- a = 1, d = 13
- a = 13, d = 1

So, the values of a, c, and d are:
- a = 1, c = 13, d = 13
- a = 13, c = 13, d = 1

These are the two possible solutions that satisfy the given conditions.

Summary:
The values of a, c, and d are either (1, 13, 13) or (13, 13, 1), depending on the specific context or problem.