19661 ÷ 3 = 6553 R2
Alright, let's work through the division of 19661 by 3 step by step.

Step 1:
3 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 3

Step 2:
3 goes into 19 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 18 from 19 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 3:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 65
Subtract 15 from 16 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 3

Step 4:
3 goes into 16 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 655
Subtract 15 from 16 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 3

Step 5:
3 goes into 11 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 6553
Subtract 9 from 11 to get 2.

The final result is 6553 with a remainder of 2.