Explanation:

To understand the question, let's first define what a two-factor product is. A two-factor product refers to the product of two distinct numbers. For example, the two-factor products of the numbers 1, 2, 3, and 4 are: 1*2, 1*3, 1*4, 2*3, 2*4, and 3*4.

Now, let's break down the problem step by step:

Step 1: Count the total number of two-factor products that can be formed from the given numbers 1, 2, 3, 4, ..., 200.
To calculate the total number of two-factor products, we need to find the number of ways we can choose 2 distinct numbers from the given set. This can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

In this case, n = 200 (total numbers given) and r = 2 (we need to choose 2 numbers).

Using the combination formula, we can calculate:

200C2 = 200! / (2! * (200-2)!) = 200! / (2! * 198!) = (200 * 199) / (2 * 1) = 19900

Therefore, there are a total of 19900 two-factor products that can be formed from the given numbers.

Step 2: Count the number of two-factor products that are multiples of 5.
To find the number of two-factor products that are multiples of 5, we need to check each two-factor product and see if it is divisible by 5.

Let's consider the factors of 5:
1 * 5 = 5
2 * 5 = 10
3 * 5 = 15
4 * 5 = 20
...
40 * 5 = 200

We can observe that there are 40 two-factor products that are multiples of 5.

Step 3: Determine the answer.
To find the answer, we need to calculate the ratio of the number of two-factor products that are multiples of 5 to the total number of two-factor products.

Ratio = (Number of two-factor products that are multiples of 5) / (Total number of two-factor products)

Ratio = 40 / 19900

Simplifying the ratio, we get:

Ratio = 2 / 995

Now, we need to find the factors of 995 and check if 2 is a factor.

Factors of 995: 1, 5, 199, 995

As we can see, 2 is not a factor of 995. Therefore, the number of factors out of the total obtained which are multiples of 5 is 0.

Hence, the correct answer is d) None of these.