3647 ÷ 6 = 607 R5
Alright, let's work through the division of 3647 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 (6) of the dividend behind the 3 and repeat the process: 36 / 6

Step 2:
6 goes into 36 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 36 from 36 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: 60
Subtract 0 from 4 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 6

Step 4:
6 goes into 47 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 607
Subtract 42 from 47 to get 5.

The final result is 607 with a remainder of 5.