We look at the division of 513574 by 19 
Let's see how many times 19 fits into 513574.

Going ahead to step 1:
The number 19 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 19

Moving on to step 2:
19 can be fit into 51 2 times, resulting in a remainder of 13.
Write down 2 as next digit of the result. 
Result so far: 2.0
If we subtract 38 from 51, we get 13.
Take the next digit (3) from the dividend and append it to 13, then repeat: 133 / 19

Moving on to step 3:
The number 19 fits into 133 7 times, leaving a remainder of 0.
Put 7 as the next digit of the answer. 
Result so far: 27.0
If we take 133 away from 133, we end up with 0.
Take the next digit (5) from the dividend and append it to 0, then repeat: 5 / 19

Going ahead to step 4:
If we divide 5 by 19, we get 0 and a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 270.0
The remainder is 5 after subtracting 0 from 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 19

On to step 5:
The number 19 fits into 57 3 times, leaving a remainder of 0.
The number 3 becomes the next digit in our result. 
Result so far: 2703.0
If we take 57 away from 57, we end up with 0.
Grab the next digit (4) from the dividend, add it to 0, then carry on: 4 / 19

Moving on to step 6:
19 goes into 4 0 times with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 27030.0
Deduct 0 from 4 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
If we divide 40 by 19, we get 2 and a remainder of 2.
The next digit of our result is 2. 
Result so far: 27030.2
If we take 38 away from 40, we end up with 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 8:
19 goes into 20 1 times with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 27030.21
The remainder is 1 after subtracting 19 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 9:
19 can be fit into 10 0 times, resulting in a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 27030.21
If we take 0 away from 10, we end up 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:
100 divided by 19 is 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 27030.2105
Deduct 95 from 100 and we're left 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.

Step 11:
50 divided by 19 is 2 with a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 27030.21052
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.

Let's proceed to step 12:
19 can be fit into 120 6 times, resulting in a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 27030.210526
The remainder is 6 after subtracting 114 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 13:
The number 19 fits into 60 3 times, leaving a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 27030.2105263
Subtracting 57 from 60 leaves us 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.

Moving on to step 14:
19 can be fit into 30 1 times, resulting in a remainder of 11.
The number 1 becomes the next digit in our result. 
Result so far: 27030.21052631
Subtracting 19 from 30 leaves us with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

The final outcome is 27030.21052631, with a leftover of 1.1e-08.