We're dividing 513204 by 34 
Our goal is to divide 513204 by 34.

Advancing to step 1:
If we divide 5 by 34, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 34

Advancing to step 2:
34 can be fit into 51 1 times, resulting in a remainder of 17.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 34 from 51 to get 17.
Bring next digit (3) of the dividend behind the 17 and repeat the process: 173 / 34

Step 3:
When dividing 173 by 34, we get 5 with a remainder of 3.
Record the quotient 5 as the next digit in the result. 
Result so far: 15.0
The remainder is 3 after subtracting 170 from 173.
Append the next digit (2) from the dividend to 3 and continue with: 32 / 34

Step 4:
32 divided by 34 is 0 with a remainder of 32.
The number 0 becomes the next digit in our result. 
Result so far: 150.0
Subtracting 0 from 32 leaves us with 32.
Grab the next digit (0) from the dividend, add it to 32, then carry on: 320 / 34

Step 5:
34 goes into 320 9 times with a remainder of 14.
The number 9 becomes the next digit in our result. 
Result so far: 1509.0
If we subtract 306 from 320, we get 14.
Grab the next digit (4) from the dividend, add it to 14, then carry on: 144 / 34

Step 6:
The number 34 fits into 144 4 times, leaving a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 15094.0
Subtract 136 from 144 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 7:
If we divide 80 by 34, we get 2 and a remainder of 12.
The next digit of our result is 2. 
Result so far: 15094.2
The remainder is 12 after subtracting 68 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 8:
34 can be fit into 120 3 times, resulting in a remainder of 18.
Put 3 as the next digit of the answer. 
Result so far: 15094.23
Subtract 102 from 120 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 9:
180 divided by 34 is 5 with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 15094.235
Subtracting 170 from 180 leaves us 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.

Let's proceed to step 10:
If we divide 100 by 34, we get 2 and a remainder of 32.
Write down 2 as next digit of the result. 
Result so far: 15094.2352
Subtracting 68 from 100 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 11:
34 goes into 320 9 times with a remainder of 14.
Use 9 as the next digit of our solution. 
Result so far: 15094.23529
Subtracting 306 from 320 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 12:
When dividing 140 by 34, we get 4 with a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 15094.235294
If we subtract 136 from 140, we 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.

Going ahead to step 13:
The number 34 fits into 40 1 times, leaving a remainder of 6.
The next digit of our result is 1. 
Result so far: 15094.2352941
The remainder is 6 after subtracting 34 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 14:
34 goes into 60 1 times with a remainder of 26.
The next digit of our result is 1. 
Result so far: 15094.23529411
Deduct 34 from 60 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

The quotient of the division is 15094.23529411, and the remainder is 2.6e-08.