35628 ÷ 6 = 5938 R0
Alright, let's work through the division of 35628 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 (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 2:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 30 from 35 to get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 6

Step 3:
6 goes into 56 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 59
Subtract 54 from 56 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 4:
6 goes into 22 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 593
Subtract 18 from 22 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: 5938
Subtract 48 from 48 to get 0.

The final result is 5938 with a remainder of 0.