66556 ÷ 3 = 22185 R1
Alright, let's work through the division of 66556 by 3 step by step.

Step 1:
3 goes into 6 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 6 from 6 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 3

Step 2:
3 goes into 6 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 22
Subtract 6 from 6 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 3

Step 3:
3 goes into 5 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 221
Subtract 3 from 5 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 3

Step 4:
3 goes into 25 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 2218
Subtract 24 from 25 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 5:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 22185
Subtract 15 from 16 to get 1.

The final result is 22185 with a remainder of 1.