Explanation:

- To find the largest number that leaves the same remainder when dividing 827, 1149, and 1310, we need to find the greatest common divisor (GCD) of their pairwise differences.

- Calculate differences:

- 1149 - 827 = 322

- 1310 - 1149 = 161

- 1310 - 827 = 483

- Find the GCD of these differences (322, 161, 483).

- The GCD of 322 and 483 is 161.

- The GCD of 161 and 161 is 161.

- Therefore, the largest number is 161.

- Option:1 161 is the correct answer.