6623 ÷ 6 = 1103 R5
Alright, let's work through the division of 6623 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 (2) of the dividend behind the 0 and repeat the process: 2 / 6

Step 3:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 110
Subtract 0 from 2 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 6

Step 4:
6 goes into 23 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 1103
Subtract 18 from 23 to get 5.

The final result is 1103 with a remainder of 5.