17128 ÷ 3 = 5709 R1
Alright, let's work through the division of 17128 by 3 step by step.

Step 1:
3 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 / 3

Step 2:
3 goes into 17 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 15 from 17 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 3

Step 3:
3 goes into 21 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 57
Subtract 21 from 21 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 3

Step 4:
3 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 570
Subtract 0 from 2 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 3

Step 5:
3 goes into 28 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 5709
Subtract 27 from 28 to get 1.

The final result is 5709 with a remainder of 1.