103872 ÷ 17 
We're looking to find how many times 17 goes into 103872.

Going ahead to step 1:
When dividing 1 by 17, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 17

Step 2:
17 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Bring next digit (3) of the dividend behind the 10 and repeat the process: 103 / 17

On to step 3:
17 goes into 103 6 times with a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 102 from 103, we get 1.
Grab the next digit (8) from the dividend, add it to 1, then carry on: 18 / 17

Advancing to step 4:
The number 17 fits into 18 1 times, leaving a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 61.0
Subtract 17 from 18 to get 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 17

Step 5:
17 goes into 17 1 times with a remainder of 0.
Use 1 as the next digit of our solution. 
Result so far: 611.0
If we subtract 17 from 17, we get 0.
Grab the next digit (2) from the dividend, add it to 0, then carry on: 2 / 17

Advancing to step 6:
If we divide 2 by 17, we get 0 and a remainder of 2.
Put 0 as the next digit of the answer. 
Result so far: 6110.0
Subtract 0 from 2 to 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.

Advancing to step 7:
20 divided by 17 is 1 with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 6110.1
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.

Advancing to step 8:
The number 17 fits into 30 1 times, leaving a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 6110.11
The remainder is 13 after subtracting 17 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Our division results in 6110.11 with a remaining 0.013.