6671 ÷ 2 = 3335 R1
Alright, let's work through the division of 6671 by 2 step by step.

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

Step 2:
2 goes into 6 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 33
Subtract 6 from 6 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 2

Step 3:
2 goes into 7 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 333
Subtract 6 from 7 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 2

Step 4:
2 goes into 11 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 3335
Subtract 10 from 11 to get 1.

The final result is 3335 with a remainder of 1.