I'm trying to find all solutions to this system of congruences:

x = 1(mod 2) (sorry, I'm using = instead of the logical equivalence)

x = 2(mod 3)

x = 3(mod 5)

x = 4(mod 11)

2 * 3 * 5 * 11 = 330

M1 = m / 2 = 165 (3 * 5 * 11)

M2 = m / 3 = 110 (2 * 5 * 11)

M3 = m / 5 = 66 (2 * 3 * 11)

M4 = m /11 = 30 (2 * 3 * 5) (I think this is where my problem is)

165 = 1(mod 2)

110 = 1(mod 3)

66 = 1(mod 5)

30 = 8(mod 11)

x = 1 * 165 * 1 + 2 * 110 * 2 + 3 * 66 * 1 + 4 * 30 * 8 = 1763

1763 = 113(mod 330)

x = 113 holds up for the first three congruences, but fails on the 4th.

Could someone please point out where I'm going wrong? I have no problem solving the system with the first three congruences, but every time I add the fourth and try to solve it, I run into problems.