We look at the division of 508565 by 76 
Our goal is to divide 508565 by 76.

On to step 1:
76 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.
Append the next digit (0) from the dividend to 5 and continue with: 50 / 76

Step 2:
76 goes into 50 0 times with a remainder of 50.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 50 leaves us with 50.
Fetch the next digit (8) from the dividend, attach it to 50 and continue: 508 / 76

Going ahead to step 3:
76 can be fit into 508 6 times, resulting in a remainder of 52.
Write down 6 as next digit of the result. 
Result so far: 6.0
Subtracting 456 from 508 leaves us with 52.
Take the next digit (5) from the dividend and append it to 52, then repeat: 525 / 76

Let's proceed to step 4:
When dividing 525 by 76, we get 6 with a remainder of 69.
The next digit of our result is 6. 
Result so far: 66.0
Deduct 456 from 525 and we're left with 69.
Include the next digit (6) from the dividend after 69, then repeat: 696 / 76

Moving on to step 5:
If we divide 696 by 76, we get 9 and a remainder of 12.
Use 9 as the next digit of our solution. 
Result so far: 669.0
Deduct 684 from 696 and we're left with 12.
Bring next digit (5) of the dividend behind the 12 and repeat the process: 125 / 76

On to step 6:
125 divided by 76 is 1 with a remainder of 49.
Write down 1 as next digit of the result. 
Result so far: 6691.0
Subtract 76 from 125 to get 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

On to step 7:
76 can be fit into 490 6 times, resulting in a remainder of 34.
Use 6 as the next digit of our solution. 
Result so far: 6691.6
Subtract 456 from 490 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 8:
When dividing 340 by 76, we get 4 with a remainder of 36.
Record the quotient 4 as the next digit in the result. 
Result so far: 6691.64
Subtract 304 from 340 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 9:
The number 76 fits into 360 4 times, leaving a remainder of 56.
The number 4 becomes the next digit in our result. 
Result so far: 6691.644
Subtract 304 from 360 to get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

The final result is 6691.644 with a remainder of 0.0056.