33768 ÷ 6 = 5628 R0
Alright, let's work through the division of 33768 by 6 step by step.

Step 1:
6 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 2:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 30 from 33 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 3:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 56
Subtract 36 from 37 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 6

Step 4:
6 goes into 16 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 562
Subtract 12 from 16 to get 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 6

Step 5:
6 goes into 48 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 5628
Subtract 48 from 48 to get 0.

The final result is 5628 with a remainder of 0.