38641 ÷ 6 = 6440 R1
Alright, let's work through the division of 38641 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 (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 2:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 36 from 38 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 6

Step 3:
6 goes into 26 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 64
Subtract 24 from 26 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 6

Step 4:
6 goes into 24 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 644
Subtract 24 from 24 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 5:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 6440
Subtract 0 from 1 to get 1.

The final result is 6440 with a remainder of 1.