We look at the division of 516839 by 43 
We're looking to find how many times 43 goes into 516839.

Let's proceed to step 1:
When dividing 5 by 43, we get 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 43

Going ahead to step 2:
43 goes into 51 1 times with a remainder of 8.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 43 from 51 leaves us with 8.
Append the next digit (6) from the dividend to 8 and continue with: 86 / 43

Advancing to step 3:
When dividing 86 by 43, we get 2 with a remainder of 0.
The next digit of our result is 2. 
Result so far: 12.0
If we take 86 away from 86, we end up with 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 43

Let's proceed to step 4:
43 goes into 8 0 times with a remainder of 8.
The next digit of our result is 0. 
Result so far: 120.0
If we subtract 0 from 8, we get 8.
Fetch the next digit (3) from the dividend, attach it to 8 and continue: 83 / 43

Moving on to step 5:
The number 43 fits into 83 1 times, leaving a remainder of 40.
The number 1 becomes the next digit in our result. 
Result so far: 1201.0
Deduct 43 from 83 and we're left with 40.
Fetch the next digit (9) from the dividend, attach it to 40 and continue: 409 / 43

Going ahead to step 6:
43 goes into 409 9 times with a remainder of 22.
Put 9 as the next digit of the answer. 
Result so far: 12019.0
Subtracting 387 from 409 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.

Step 7:
The number 43 fits into 220 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 12019.5
Deduct 215 from 220 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
43 goes into 50 1 times with a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 12019.51
Subtract 43 from 50 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 9:
43 goes into 70 1 times with a remainder of 27.
Use 1 as the next digit of our solution. 
Result so far: 12019.511
If we take 43 away from 70, we end up with 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

The quotient of the division is 12019.511, and the remainder is 0.0027.