The number of prime numbers among the given numbers can be determined by analyzing each number individually and checking if it is a prime number or not.

Prime numbers are defined as numbers that are greater than 1 and have no divisors other than 1 and themselves. Therefore, to determine if a number is prime, we need to check if it is divisible by any number other than 1 and itself.

Let's analyze each number individually:

1. 105!:
105! is the product of all positive integers from 1 to 105. It is a very large number, and it is not feasible to manually check if it is prime or not. However, we can make some observations:

- 105! is divisible by 2, 3, 4, 5, 6, ..., 105, as it includes all those numbers in its calculation.
- Therefore, we can conclude that 105! is not a prime number.

2. 2,105!:
2,105! is also a very large number, and it is not feasible to manually check if it is prime or not. However, we can make similar observations as before:

- 2,105! is divisible by 2, 3, 4, 5, 6, ..., 105, as it includes all those numbers in its calculation.
- Therefore, we can conclude that 2,105! is not a prime number.

3. 3,105!:
Similarly, 3,105! is a very large number and can be observed to be divisible by numbers from 2 to 105.
- Therefore, 3,105! is not a prime number.

4. 4,105!:
Again, 4,105! is a large number and can be observed to be divisible by numbers from 2 to 105.
- Therefore, 4,105! is not a prime number.

5. 104,105!:
104,105! is a large number and can be observed to be divisible by numbers from 2 to 105.
- Therefore, 104,105! is not a prime number.

6. 105:
105 is not divisible by any number other than 1 and itself.
- Therefore, 105 is a prime number.

Based on the analysis above, we can conclude that there is only one prime number among the given numbers, which is 105 (option A).

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