We're dividing 32517 by 19 
We want to divide 32517 by 19.

On to step 1:
When dividing 3 by 19, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Fetch the next digit (2) from the dividend, attach it to 3 and continue: 32 / 19

On to step 2:
If we divide 32 by 19, we get 1 and a remainder of 13.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtract 19 from 32 to get 13.
Bring next digit (5) of the dividend behind the 13 and repeat the process: 135 / 19

On to step 3:
135 divided by 19 is 7 with a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 17.0
Subtract 133 from 135 to get 2.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 19

On to step 4:
The number 19 fits into 21 1 times, leaving a remainder of 2.
The next digit of our result is 1. 
Result so far: 171.0
Subtract 19 from 21 to get 2.
Include the next digit (7) from the dividend after 2, then repeat: 27 / 19

Going ahead to step 5:
When dividing 27 by 19, we get 1 with a remainder of 8.
Use 1 as the next digit of our solution. 
Result so far: 1711.0
The remainder is 8 after subtracting 19 from 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 6:
If we divide 80 by 19, we get 4 and a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 1711.4
The remainder is 4 after subtracting 76 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 7:
40 divided by 19 is 2 with a remainder of 2.
Record the quotient 2 as the next digit in the result. 
Result so far: 1711.42
The remainder is 2 after subtracting 38 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 8:
When dividing 20 by 19, we get 1 with a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 1711.421
If we take 19 away from 20, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 9:
If we divide 10 by 19, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 1711.421
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 10:
If we divide 100 by 19, we get 5 and a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 1711.42105
If we subtract 95 from 100, we get 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 11:
If we divide 50 by 19, we get 2 and a remainder of 12.
The number 2 becomes the next digit in our result. 
Result so far: 1711.421052
If we take 38 away from 50, we end up with 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 12:
19 goes into 120 6 times with a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 1711.4210526
Deduct 114 from 120 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 13:
The number 19 fits into 60 3 times, leaving a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 1711.42105263
If we take 57 away from 60, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

After the division, we end up with 1711.42105263 and a remainder of 3e-09.