6643 ÷ 6 = 1107 R1
Alright, let's work through the division of 6643 by 6 step by step.

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

Step 2:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 6 from 6 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 6

Step 3:
6 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 110
Subtract 0 from 4 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

Step 4:
6 goes into 43 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 1107
Subtract 42 from 43 to get 1.

The final result is 1107 with a remainder of 1.