We look at the division of 82557 by 17 
We're looking to find how many times 17 goes into 82557.

On to step 1:
The number 17 fits into 8 0 times, leaving a remainder of 8.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Fetch the next digit (2) from the dividend, attach it to 8 and continue: 82 / 17

On to step 2:
The number 17 fits into 82 4 times, leaving a remainder of 14.
Use 4 as the next digit of our solution. 
Result so far: 4.0
If we subtract 68 from 82, we get 14.
Bring next digit (5) of the dividend behind the 14 and repeat the process: 145 / 17

On to step 3:
145 divided by 17 is 8 with a remainder of 9.
Write down 8 as next digit of the result. 
Result so far: 48.0
If we subtract 136 from 145, we get 9.
Bring next digit (5) of the dividend behind the 9 and repeat the process: 95 / 17

Step 4:
17 can be fit into 95 5 times, resulting in a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 485.0
If we take 85 away from 95, we end up with 10.
Grab the next digit (7) from the dividend, add it to 10, then carry on: 107 / 17

On to step 5:
When dividing 107 by 17, we get 6 with a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 4856.0
If we take 102 away from 107, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 6:
50 divided by 17 is 2 with a remainder of 16.
Use 2 as the next digit of our solution. 
Result so far: 4856.2
Subtract 34 from 50 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 7:
If we divide 160 by 17, we get 9 and a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 4856.29
Deduct 153 from 160 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 8:
17 can be fit into 70 4 times, resulting in a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 4856.294
If we subtract 68 from 70, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 9:
17 goes into 20 1 times with a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 4856.2941
Subtract 17 from 20 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 10:
When dividing 30 by 17, we get 1 with a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 4856.29411
If we take 17 away from 30, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The quotient of the division is 4856.29411, and the remainder is 1.3e-05.