81319 ÷ 6 = 13553 R1
Alright, let's work through the division of 81319 by 6 step by step.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 2:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 21 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 3:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 135
Subtract 30 from 33 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 6

Step 4:
6 goes into 31 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 1355
Subtract 30 from 31 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 6

Step 5:
6 goes into 19 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 13553
Subtract 18 from 19 to get 1.

The final result is 13553 with a remainder of 1.