508097 ÷ 4 
The aim is to understand the frequency of 4 in 508097.

Advancing to step 1:
If we divide 5 by 4, we get 1 and a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 4 from 5 and we're left with 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 4

Let's proceed to step 2:
If we divide 10 by 4, we get 2 and a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Subtract 8 from 10 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 4

Step 3:
If we divide 28 by 4, we get 7 and a remainder of 0.
Record the quotient 7 as the next digit in the result. 
Result so far: 127.0
The remainder is 0 after subtracting 28 from 28.
Include the next digit (0) from the dividend after 0, then repeat: 0 / 4

Step 4:
0 divided by 4 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 1270.0
Subtracting 0 from 0 leaves us with 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 4

Step 5:
If we divide 9 by 4, we get 2 and a remainder of 1.
Put 2 as the next digit of the answer. 
Result so far: 12702.0
If we take 8 away from 9, we end up with 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 4

Step 6:
4 goes into 17 4 times with a remainder of 1.
Record the quotient 4 as the next digit in the result. 
Result so far: 127024.0
If we subtract 16 from 17, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
4 goes into 10 2 times with a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 127024.2
If we subtract 8 from 10, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 8:
4 goes into 20 5 times with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 127024.25
Subtracting 20 from 20 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.

Advancing to step 9:
4 can be fit into 0 0 times, resulting in a remainder of 0.
The next digit of our result is 0. 
Result so far: 127024.25
If we take 0 away from 0, we end up 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.

Step 10:
The number 4 fits into 0 0 times, leaving a remainder of 0.
The next digit of our result is 0. 
Result so far: 127024.25
If we take 0 away from 0, we end up 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.

In conclusion, the division gives 127024.25 with a balance of 0.0.