Explanation:

To determine the greatest number that leaves a remainder of 6 when 156, 181, and 331 are divided by it, follow these steps:

- Subtract 6 from each number to get dividends:

- 150 from 156

- 175 from 181

- 325 from 331

- Now, find the greatest common divisor (GCD) of 150, 175, and 325.

- Calculate GCD as follows:

- Prime factorization:

- 150 = \(2 \times 3 \times 5^2\)

- 175 = \(5^2 \times 7\)

- 325 = \(5^2 \times 13\)

- The common factor is \(5^2\), which is 25.

- Thus, the greatest number by which the numbers can be divided to leave a remainder of 6 is 25.

- Option 3: 25 is the correct answer.