Based on the given information, we know that the product of the integers a, b, c, and d is 1,155.

We also know that a < b="" />< c="" />< />

To find the values of a, b, c, and d, we can start by finding the prime factorization of 1,155.

The prime factorization of 1,155 is 3 * 5 * 7 * 11.

Since a < b="" />< c="" />< d,="" we="" need="" to="" distribute="" these="" prime="" factors="" in="" ascending="" order="" among="" the="" />

Let's start with the smallest prime factor, which is 3.

We have three possibilities for distributing the factor of 3 among the integers:

1. a = 3, b = 1, c = 1, d = 385
2. a = 1, b = 3, c = 1, d = 385
3. a = 1, b = 1, c = 3, d = 385

Next, let's consider the next smallest prime factor, which is 5.

We can distribute the factor of 5 among the integers in the following ways:

1. a = 3, b = 5, c = 1, d = 77
2. a = 3, b = 1, c = 5, d = 77
3. a = 1, b = 3, c = 5, d = 77

Now let's consider the next prime factor, which is 7.

We can distribute the factor of 7 among the integers in the following ways:

1. a = 3, b = 5, c = 7, d = 11
2. a = 3, b = 7, c = 5, d = 11
3. a = 3, b = 7, c = 11, d = 5
4. a = 5, b = 3, c = 7, d = 11
5. a = 5, b = 7, c = 3, d = 11
6. a = 5, b = 7, c = 11, d = 3
7. a = 7, b = 3, c = 5, d = 11
8. a = 7, b = 5, c = 3, d = 11
9. a = 7, b = 5, c = 11, d = 3

Finally, let's consider the last prime factor, which is 11.

We can distribute the factor of 11 among the integers in the following ways:

1. a = 3, b = 5, c = 7, d = 11
2. a = 3, b = 7, c = 5, d = 11
3. a = 3, b = 7, c = 11, d = 5
4. a = 5, b = 3, c = 7, d = 11
5. a = 5, b = 7, c = 3, d = 11
6. a = 5, b = 7, c = 11, d = 3
7.