We're dividing 565767 by 84 
Our goal is to divide 565767 by 84.

Let's proceed to step 1:
The number 84 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 subtract 0 from 5, we get 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 84

Moving on to step 2:
The number 84 fits into 56 0 times, leaving a remainder of 56.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 56, we get 56.
Fetch the next digit (5) from the dividend, attach it to 56 and continue: 565 / 84

Step 3:
If we divide 565 by 84, we get 6 and a remainder of 61.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Deduct 504 from 565 and we're left with 61.
Append the next digit (7) from the dividend to 61 and continue with: 617 / 84

Step 4:
617 divided by 84 is 7 with a remainder of 29.
Write down 7 as next digit of the result. 
Result so far: 67.0
If we take 588 away from 617, we end up with 29.
Append the next digit (6) from the dividend to 29 and continue with: 296 / 84

On to step 5:
When dividing 296 by 84, we get 3 with a remainder of 44.
Record the quotient 3 as the next digit in the result. 
Result so far: 673.0
Deduct 252 from 296 and we're left with 44.
Bring next digit (7) of the dividend behind the 44 and repeat the process: 447 / 84

On to step 6:
447 divided by 84 is 5 with a remainder of 27.
Use 5 as the next digit of our solution. 
Result so far: 6735.0
If we subtract 420 from 447, we 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.

Going ahead to step 7:
When dividing 270 by 84, we get 3 with a remainder of 18.
The next digit of our result is 3. 
Result so far: 6735.3
If we subtract 252 from 270, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 8:
180 divided by 84 is 2 with a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 6735.32
Subtract 168 from 180 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 9:
84 can be fit into 120 1 times, resulting in a remainder of 36.
Write down 1 as next digit of the result. 
Result so far: 6735.321
Subtracting 84 from 120 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 10:
84 goes into 360 4 times with a remainder of 24.
Use 4 as the next digit of our solution. 
Result so far: 6735.3214
Subtracting 336 from 360 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 11:
240 divided by 84 is 2 with a remainder of 72.
The number 2 becomes the next digit in our result. 
Result so far: 6735.32142
The remainder is 72 after subtracting 168 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Step 12:
When dividing 720 by 84, we get 8 with a remainder of 48.
Write down 8 as next digit of the result. 
Result so far: 6735.321428
If we take 672 away from 720, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 13:
84 goes into 480 5 times with a remainder of 60.
Use 5 as the next digit of our solution. 
Result so far: 6735.3214285
Deduct 420 from 480 and we're left with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 14:
84 goes into 600 7 times with a remainder of 12.
Write down 7 as next digit of the result. 
Result so far: 6735.32142857
Subtract 588 from 600 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final result is 6735.32142857 with a remainder of 1.2e-08.