7817 ÷ 6 = 1302 R5
Alright, let's work through the division of 7817 by 6 step by step.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 6

Step 2:
6 goes into 18 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 18 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 6

Step 3:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 130
Subtract 0 from 1 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 6

Step 4:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 1302
Subtract 12 from 17 to get 5.

The final result is 1302 with a remainder of 5.