We notice that each term in the sequence is a perfect cube: $6075 = 3^5 \cdot 5^2$, $2025 = 3^4 \cdot 5^2$, $675 = 3^3 \cdot 5^2$, and so on.
To find the number of integers in the sequence, we need to find the largest exponent of 3 that divides each term.
For the first term, $3^5$ divides evenly, so the largest exponent of 3 is 5.
For the second term, $3^4$ divides evenly, so the largest exponent of 3 is 4.
For the third term, $3^3$ divides evenly, so the largest exponent of 3 is 3.
We can continue this pattern and see that the largest exponent of 3 decreases by 1 for each term.
Therefore, there are $\boxed{6}$ integers in this sequence.The answer is: 6
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The sequence $6075, 2025, 675 \ldots$, is made by repeatedly dividing by 3. How many integers are in this sequence?

### Answer:
