31963 ÷ 6 = 5327 R1
Alright, let's work through the division of 31963 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 (1) of the dividend behind the 3 and repeat the process: 31 / 6

Step 2:
6 goes into 31 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 30 from 31 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 6

Step 3:
6 goes into 19 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 53
Subtract 18 from 19 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: 532
Subtract 12 from 16 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

Step 5:
6 goes into 43 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 5327
Subtract 42 from 43 to get 1.

The final result is 5327 with a remainder of 1.