8666 ÷ 3 = 2888 R2
Let's divide 8666 by 3.

Step 1:
3 goes into 8 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 6 from 8 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 3

Step 2:
3 goes into 26 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 28
Subtract 24 from 26 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 3

Step 3:
3 goes into 26 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 288
Subtract 24 from 26 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 3

Step 4:
3 goes into 26 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 2888
Subtract 24 from 26 to get 2.

The final result is 2888 with a remainder of 2.