Answer :

Final answer:

The greatest number by which 156, 181, and 331 each have a remainder of 6 when divided is 25, which is found using the Euclidean algorithm to calculate the greatest common divisor.

Explanation:

The question is asking for the greatest number by which 156, 181 and 331 leave a remainder of 6 when divided. To find this number, we first need to subtract 6 from each number, getting 150, 175, and 325. According to the Euclidean algorithm, the largest number that can divide these numbers is found by calculating the greatest common divisor (GCD). We find that the GCD of 150, 175, and 325 is 25. Therefore, when 156, 181, and 331 are divided by 25, the remainder in each case is 6.

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