We look at the division of 17165327 by 338 
We want to figure out the number of times 17165327 can be divided by 338.

Going ahead to step 1:
338 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 338

Going ahead to step 2:
If we divide 17 by 338, we get 0 and a remainder of 17.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 17 leaves us with 17.
Take the next digit (1) from the dividend and append it to 17, then repeat: 171 / 338

Advancing to step 3:
If we divide 171 by 338, we get 0 and a remainder of 171.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 171 to get 171.
Take the next digit (6) from the dividend and append it to 171, then repeat: 1716 / 338

Going ahead to step 4:
The number 338 fits into 1716 5 times, leaving a remainder of 26.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtract 1690 from 1716 to get 26.
Grab the next digit (5) from the dividend, add it to 26, then carry on: 265 / 338

On to step 5:
338 can be fit into 265 0 times, resulting in a remainder of 265.
Record the quotient 0 as the next digit in the result. 
Result so far: 50.0
Subtract 0 from 265 to get 265.
Include the next digit (3) from the dividend after 265, then repeat: 2653 / 338

Advancing to step 6:
The number 338 fits into 2653 7 times, leaving a remainder of 287.
The number 7 becomes the next digit in our result. 
Result so far: 507.0
If we subtract 2366 from 2653, we get 287.
Take the next digit (2) from the dividend and append it to 287, then repeat: 2872 / 338

Moving on to step 7:
2872 divided by 338 is 8 with a remainder of 168.
Record the quotient 8 as the next digit in the result. 
Result so far: 5078.0
If we take 2704 away from 2872, we end up with 168.
Bring next digit (7) of the dividend behind the 168 and repeat the process: 1687 / 338

On to step 8:
The number 338 fits into 1687 4 times, leaving a remainder of 335.
Use 4 as the next digit of our solution. 
Result so far: 50784.0
If we subtract 1352 from 1687, we get 335.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3350, and continue the process.

Let's proceed to step 9:
When dividing 3350 by 338, we get 9 with a remainder of 308.
Use 9 as the next digit of our solution. 
Result so far: 50784.9
Deduct 3042 from 3350 and we're left with 308.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3080, and continue the process.

Going ahead to step 10:
338 goes into 3080 9 times with a remainder of 38.
Put 9 as the next digit of the answer. 
Result so far: 50784.99
The remainder is 38 after subtracting 3042 from 3080.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

The quotient of the division is 50784.99, and the remainder is 0.038.