17282 ÷ 6 = 2880 R2
Alright, let's work through the division of 17282 by 6 step by step.

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

Step 2:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 12 from 17 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 6

Step 3:
6 goes into 52 8 times with a remainder of 4.
Write down 8 as next digit of of the result. 
Result so far: 28
Subtract 48 from 52 to get 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 6

Step 4:
6 goes into 48 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 288
Subtract 48 from 48 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 6

Step 5:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 2880
Subtract 0 from 2 to get 2.

The final result is 2880 with a remainder of 2.