We're dividing 513354 by 34 
We're looking to find how many times 34 goes into 513354.

Moving on to step 1:
34 goes into 5 0 times with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 34

Moving on to step 2:
When dividing 51 by 34, we get 1 with a remainder of 17.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 34 from 51 to get 17.
Fetch the next digit (3) from the dividend, attach it to 17 and continue: 173 / 34

Going ahead to step 3:
When dividing 173 by 34, we get 5 with a remainder of 3.
The number 5 becomes the next digit in our result. 
Result so far: 15.0
If we subtract 170 from 173, we get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 34

Let's proceed to step 4:
34 can be fit into 33 0 times, resulting in a remainder of 33.
The next digit of our result is 0. 
Result so far: 150.0
If we subtract 0 from 33, we get 33.
Include the next digit (5) from the dividend after 33, then repeat: 335 / 34

On to step 5:
335 divided by 34 is 9 with a remainder of 29.
Record the quotient 9 as the next digit in the result. 
Result so far: 1509.0
Deduct 306 from 335 and we're left with 29.
Grab the next digit (4) from the dividend, add it to 29, then carry on: 294 / 34

On to step 6:
The number 34 fits into 294 8 times, leaving a remainder of 22.
Use 8 as the next digit of our solution. 
Result so far: 15098.0
The remainder is 22 after subtracting 272 from 294.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 7:
220 divided by 34 is 6 with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 15098.6
Subtracting 204 from 220 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 8:
34 can be fit into 160 4 times, resulting in a remainder of 24.
Use 4 as the next digit of our solution. 
Result so far: 15098.64
Subtract 136 from 160 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 9:
34 can be fit into 240 7 times, resulting in a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 15098.647
If we take 238 away from 240, 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 10:
34 goes into 20 0 times with a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 15098.647
Deduct 0 from 20 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 11:
34 goes into 200 5 times with a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 15098.64705
Subtract 170 from 200 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 12:
300 divided by 34 is 8 with a remainder of 28.
Use 8 as the next digit of our solution. 
Result so far: 15098.647058
Subtract 272 from 300 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 13:
34 goes into 280 8 times with a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 15098.6470588
If we take 272 away from 280, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Our division results in 15098.6470588 with a remaining 8e-08.