513533 ÷ 71 
Our goal is to divide 513533 by 71.

On to step 1:
71 goes into 5 0 times with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 71

On to step 2:
If we divide 51 by 71, we get 0 and a remainder of 51.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 51, we end up with 51.
Include the next digit (3) from the dividend after 51, then repeat: 513 / 71

Step 3:
513 divided by 71 is 7 with a remainder of 16.
The next digit of our result is 7. 
Result so far: 7.0
If we take 497 away from 513, we end up with 16.
Append the next digit (5) from the dividend to 16 and continue with: 165 / 71

On to step 4:
If we divide 165 by 71, we get 2 and 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.
Bring next digit (3) of the dividend behind the 23 and repeat the process: 233 / 71

Going ahead to step 5:
When dividing 233 by 71, we get 3 with a remainder of 20.
Write down 3 as next digit of the result. 
Result so far: 723.0
Deduct 213 from 233 and we're left with 20.
Include the next digit (3) from the dividend after 20, then repeat: 203 / 71

Let's proceed to step 6:
203 divided by 71 is 2 with a remainder of 61.
The next digit of our result is 2. 
Result so far: 7232.0
Subtract 142 from 203 to get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

On to step 7:
The number 71 fits into 610 8 times, leaving a remainder of 42.
The next digit of our result is 8. 
Result so far: 7232.8
If we subtract 568 from 610, we get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 8:
The number 71 fits into 420 5 times, leaving a remainder of 65.
The number 5 becomes the next digit in our result. 
Result so far: 7232.85
The remainder is 65 after subtracting 355 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

Step 9:
The number 71 fits into 650 9 times, leaving a remainder of 11.
Put 9 as the next digit of the answer. 
Result so far: 7232.859
If we take 639 away from 650, we end up 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.

Let's proceed to step 10:
110 divided by 71 is 1 with a remainder of 39.
Use 1 as the next digit of our solution. 
Result so far: 7232.8591
The remainder is 39 after subtracting 71 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Going ahead to step 11:
When dividing 390 by 71, we get 5 with a remainder of 35.
The next digit of our result is 5. 
Result so far: 7232.85915
Deduct 355 from 390 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 12:
71 can be fit into 350 4 times, resulting in a remainder of 66.
Use 4 as the next digit of our solution. 
Result so far: 7232.859154
If we take 284 away from 350, we end up with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Moving on to step 13:
When dividing 660 by 71, we get 9 with a remainder of 21.
Use 9 as the next digit of our solution. 
Result so far: 7232.8591549
If we take 639 away from 660, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Step 14:
The number 71 fits into 210 2 times, leaving a remainder of 68.
The next digit of our result is 2. 
Result so far: 7232.85915492
Subtracting 142 from 210 leaves us with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

After the division, we end up with 7232.85915492 and a remainder of 6.8e-08.