We look at the division of 513597 by 71 
We're looking to find how many times 71 goes into 513597.

Advancing to step 1:
When dividing 5 by 71, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 71

Step 2:
71 can be fit into 51 0 times, resulting in a remainder of 51.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 51 after subtracting 0 from 51.
Fetch the next digit (3) from the dividend, attach it to 51 and continue: 513 / 71

Let's proceed to step 3:
If we divide 513 by 71, we get 7 and a remainder of 16.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we subtract 497 from 513, we get 16.
Bring next digit (5) of the dividend behind the 16 and repeat the process: 165 / 71

Let's proceed to step 4:
71 can be fit into 165 2 times, resulting in a remainder of 23.
Write down 2 as next digit of the result. 
Result so far: 72.0
Subtracting 142 from 165 leaves us with 23.
Grab the next digit (9) from the dividend, add it to 23, then carry on: 239 / 71

Let's proceed to step 5:
The number 71 fits into 239 3 times, leaving a remainder of 26.
Use 3 as the next digit of our solution. 
Result so far: 723.0
If we subtract 213 from 239, we get 26.
Include the next digit (7) from the dividend after 26, then repeat: 267 / 71

Going ahead to step 6:
71 can be fit into 267 3 times, resulting in a remainder of 54.
Record the quotient 3 as the next digit in the result. 
Result so far: 7233.0
The remainder is 54 after subtracting 213 from 267.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Moving on to step 7:
71 goes into 540 7 times with a remainder of 43.
The number 7 becomes the next digit in our result. 
Result so far: 7233.7
If we subtract 497 from 540, we get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Step 8:
If we divide 430 by 71, we get 6 and a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 7233.76
The remainder is 4 after subtracting 426 from 430.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
When dividing 40 by 71, we get 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 7233.76
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 10:
71 goes into 400 5 times with a remainder of 45.
Use 5 as the next digit of our solution. 
Result so far: 7233.7605
Subtract 355 from 400 to get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Advancing to step 11:
The number 71 fits into 450 6 times, leaving a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 7233.76056
The remainder is 24 after subtracting 426 from 450.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 12:
If we divide 240 by 71, we get 3 and a remainder of 27.
Record the quotient 3 as the next digit in the result. 
Result so far: 7233.760563
Subtract 213 from 240 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

On to step 13:
If we divide 270 by 71, we get 3 and a remainder of 57.
The number 3 becomes the next digit in our result. 
Result so far: 7233.7605633
The remainder is 57 after subtracting 213 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

In conclusion, the division gives 7233.7605633 with a balance of 5.7e-07.