We look at the division of 514561 by 84 
Our goal is to divide 514561 by 84.

Advancing to step 1:
When dividing 5 by 84, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 84

Let's proceed to step 2:
84 goes into 51 0 times with a remainder of 51.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 51 leaves us with 51.
Include the next digit (4) from the dividend after 51, then repeat: 514 / 84

Moving on to step 3:
If we divide 514 by 84, we get 6 and a remainder of 10.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
Subtracting 504 from 514 leaves us with 10.
Include the next digit (5) from the dividend after 10, then repeat: 105 / 84

On to step 4:
The number 84 fits into 105 1 times, leaving a remainder of 21.
The number 1 becomes the next digit in our result. 
Result so far: 61.0
If we subtract 84 from 105, we get 21.
Append the next digit (6) from the dividend to 21 and continue with: 216 / 84

Going ahead to step 5:
216 divided by 84 is 2 with a remainder of 48.
The next digit of our result is 2. 
Result so far: 612.0
Deduct 168 from 216 and we're left with 48.
Include the next digit (1) from the dividend after 48, then repeat: 481 / 84

Step 6:
When dividing 481 by 84, we get 5 with a remainder of 61.
Write down 5 as next digit of the result. 
Result so far: 6125.0
If we take 420 away from 481, 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.

Step 7:
The number 84 fits into 610 7 times, leaving a remainder of 22.
The number 7 becomes the next digit in our result. 
Result so far: 6125.7
If we take 588 away from 610, we end up 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.

On to step 8:
If we divide 220 by 84, we get 2 and a remainder of 52.
Use 2 as the next digit of our solution. 
Result so far: 6125.72
Subtract 168 from 220 to get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Moving on to step 9:
520 divided by 84 is 6 with a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 6125.726
Subtracting 504 from 520 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.

Let's proceed to step 10:
84 can be fit into 160 1 times, resulting in a remainder of 76.
Use 1 as the next digit of our solution. 
Result so far: 6125.7261
If we take 84 away from 160, we end up with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Moving on to step 11:
760 divided by 84 is 9 with a remainder of 4.
Write down 9 as next digit of the result. 
Result so far: 6125.72619
The remainder is 4 after subtracting 756 from 760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 12:
When dividing 40 by 84, we get 0 with a remainder of 40.
The next digit of our result is 0. 
Result so far: 6125.72619
If we take 0 away from 40, we end up 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.

On to step 13:
84 goes into 400 4 times with a remainder of 64.
Use 4 as the next digit of our solution. 
Result so far: 6125.7261904
The remainder is 64 after subtracting 336 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

On to step 14:
The number 84 fits into 640 7 times, leaving a remainder of 52.
The next digit of our result is 7. 
Result so far: 6125.72619047
If we take 588 away from 640, we end up with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Our division results in 6125.72619047 with a remaining 5.2e-08.