508551 ÷ 8 
The aim is to understand the frequency of 8 in 508551.

Advancing to step 1:
When dividing 5 by 8, we get 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 8

Going ahead to step 2:
8 can be fit into 50 6 times, resulting in a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
The remainder is 2 after subtracting 48 from 50.
Fetch the next digit (8) from the dividend, attach it to 2 and continue: 28 / 8

Moving on to step 3:
8 can be fit into 28 3 times, resulting in a remainder of 4.
Record the quotient 3 as the next digit in the result. 
Result so far: 63.0
If we subtract 24 from 28, we get 4.
Append the next digit (5) from the dividend to 4 and continue with: 45 / 8

Let's proceed to step 4:
8 can be fit into 45 5 times, resulting in a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 635.0
Subtracting 40 from 45 leaves us with 5.
Include the next digit (5) from the dividend after 5, then repeat: 55 / 8

On to step 5:
8 goes into 55 6 times with a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 6356.0
The remainder is 7 after subtracting 48 from 55.
Fetch the next digit (1) from the dividend, attach it to 7 and continue: 71 / 8

Going ahead to step 6:
If we divide 71 by 8, we get 8 and a remainder of 7.
Record the quotient 8 as the next digit in the result. 
Result so far: 63568.0
If we subtract 64 from 71, we 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.

Step 7:
8 goes into 70 8 times with a remainder of 6.
The number 8 becomes the next digit in our result. 
Result so far: 63568.8
Subtracting 64 from 70 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 8:
The number 8 fits into 60 7 times, leaving a remainder of 4.
Use 7 as the next digit of our solution. 
Result so far: 63568.87
Deduct 56 from 60 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 9:
8 goes into 40 5 times with a remainder of 0.
The next digit of our result is 5. 
Result so far: 63568.875
The remainder is 0 after subtracting 40 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 10:
If we divide 0 by 8, we get 0 and a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 63568.875
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 11:
8 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 63568.875
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 63568.875, with a leftover of 0.0.