We're dividing 512813 by 71 
We want to figure out the number of times 512813 can be divided by 71.

Step 1:
The number 71 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
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

Moving on to step 2:
71 goes into 51 0 times with a remainder of 51.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 51, we end up with 51.
Append the next digit (2) from the dividend to 51 and continue with: 512 / 71

Let's proceed to step 3:
If we divide 512 by 71, we get 7 and a remainder of 15.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtracting 497 from 512 leaves us with 15.
Include the next digit (8) from the dividend after 15, then repeat: 158 / 71

On to step 4:
71 can be fit into 158 2 times, resulting in a remainder of 16.
Write down 2 as next digit of the result. 
Result so far: 72.0
If we take 142 away from 158, we end up with 16.
Take the next digit (1) from the dividend and append it to 16, then repeat: 161 / 71

Advancing to step 5:
If we divide 161 by 71, we get 2 and a remainder of 19.
Put 2 as the next digit of the answer. 
Result so far: 722.0
The remainder is 19 after subtracting 142 from 161.
Include the next digit (3) from the dividend after 19, then repeat: 193 / 71

Moving on to step 6:
193 divided by 71 is 2 with a remainder of 51.
Use 2 as the next digit of our solution. 
Result so far: 7222.0
Subtracting 142 from 193 leaves us with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Let's proceed to step 7:
When dividing 510 by 71, we get 7 with a remainder of 13.
Record the quotient 7 as the next digit in the result. 
Result so far: 7222.7
The remainder is 13 after subtracting 497 from 510.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 8:
130 divided by 71 is 1 with a remainder of 59.
The number 1 becomes the next digit in our result. 
Result so far: 7222.71
If we take 71 away from 130, we end up with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Step 9:
The number 71 fits into 590 8 times, leaving a remainder of 22.
Put 8 as the next digit of the answer. 
Result so far: 7222.718
Subtracting 568 from 590 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 10:
If we divide 220 by 71, we get 3 and a remainder of 7.
Use 3 as the next digit of our solution. 
Result so far: 7222.7183
If we take 213 away from 220, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 11:
When dividing 70 by 71, we get 0 with a remainder of 70.
The next digit of our result is 0. 
Result so far: 7222.7183
The remainder is 70 after subtracting 0 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 12:
If we divide 700 by 71, we get 9 and a remainder of 61.
Use 9 as the next digit of our solution. 
Result so far: 7222.718309
If we take 639 away from 700, we end up with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Let's proceed to step 13:
If we divide 610 by 71, we get 8 and a remainder of 42.
Record the quotient 8 as the next digit in the result. 
Result so far: 7222.7183098
Deduct 568 from 610 and we're left with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Going ahead to step 14:
71 goes into 420 5 times with a remainder of 65.
The next digit of our result is 5. 
Result so far: 7222.71830985
If we subtract 355 from 420, we get 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

The quotient of the division is 7222.71830985, and the remainder is 6.5e-08.