3431 ÷ 6 = 571 R5
Alright, let's work through the division of 3431 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 (4) of the dividend behind the 3 and repeat the process: 34 / 6

Step 2:
6 goes into 34 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 30 from 34 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

Step 3:
6 goes into 43 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 57
Subtract 42 from 43 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 6

Step 4:
6 goes into 11 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 571
Subtract 6 from 11 to get 5.

The final result is 571 with a remainder of 5.