We look at the division of 338260 by 17 
We want to figure out the number of times 338260 can be divided by 17.

Advancing to step 1:
17 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 17

On to step 2:
The number 17 fits into 33 1 times, leaving a remainder of 16.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 17 from 33, we get 16.
Take the next digit (8) from the dividend and append it to 16, then repeat: 168 / 17

Advancing to step 3:
168 divided by 17 is 9 with a remainder of 15.
Record the quotient 9 as the next digit in the result. 
Result so far: 19.0
Subtract 153 from 168 to get 15.
Include the next digit (2) from the dividend after 15, then repeat: 152 / 17

Moving on to step 4:
152 divided by 17 is 8 with a remainder of 16.
The next digit of our result is 8. 
Result so far: 198.0
Subtracting 136 from 152 leaves us with 16.
Include the next digit (6) from the dividend after 16, then repeat: 166 / 17

Moving on to step 5:
The number 17 fits into 166 9 times, leaving a remainder of 13.
Use 9 as the next digit of our solution. 
Result so far: 1989.0
If we take 153 away from 166, we end up with 13.
Grab the next digit (0) from the dividend, add it to 13, then carry on: 130 / 17

On to step 6:
The number 17 fits into 130 7 times, leaving a remainder of 11.
Write down 7 as next digit of the result. 
Result so far: 19897.0
Subtract 119 from 130 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 7:
17 can be fit into 110 6 times, resulting in a remainder of 8.
The next digit of our result is 6. 
Result so far: 19897.6
Subtracting 102 from 110 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 8:
If we divide 80 by 17, we get 4 and a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 19897.64
If we subtract 68 from 80, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 9:
17 can be fit into 120 7 times, resulting in a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 19897.647
The remainder is 1 after subtracting 119 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 10:
10 divided by 17 is 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 19897.647
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 11:
17 goes into 100 5 times with a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 19897.64705
The remainder is 15 after subtracting 85 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 12:
17 goes into 150 8 times with a remainder of 14.
Write down 8 as next digit of the result. 
Result so far: 19897.647058
If we subtract 136 from 150, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 13:
17 can be fit into 140 8 times, resulting in a remainder of 4.
The next digit of our result is 8. 
Result so far: 19897.6470588
Subtract 136 from 140 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

After the division, we end up with 19897.6470588 and a remainder of 4e-08.