jmc

The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, and 342. The factors of 285 are 1, 3, 5, 15, 19, 57, 95, and 285. By comparing the two lists, we can see that the numbers that are factors of both 342 and 285 are 1, 3, 19, and 57. So, the largest divisor of both 342 and 285 is $\boxed{57}$.