82309 ÷ 6 = 13718 R1
We're going to perform division on 82309 with 6 as the divisor.

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 (2) of the dividend behind the 2 and repeat the process: 22 / 6

Step 2:
6 goes into 22 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 22 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: 137
Subtract 42 from 43 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 4:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1371
Subtract 6 from 10 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 6

Step 5:
6 goes into 49 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 13718
Subtract 48 from 49 to get 1.

The final result is 13718 with a remainder of 1.