We're dividing 506905 by 81 
The aim is to understand the frequency of 81 in 506905.

Going ahead to step 1:
If we divide 5 by 81, we get 0 and a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Include the next digit (0) from the dividend after 5, then repeat: 50 / 81

Advancing to step 2:
50 divided by 81 is 0 with a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 50 leaves us with 50.
Include the next digit (6) from the dividend after 50, then repeat: 506 / 81

Going ahead to step 3:
The number 81 fits into 506 6 times, leaving a remainder of 20.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
Subtract 486 from 506 to get 20.
Take the next digit (9) from the dividend and append it to 20, then repeat: 209 / 81

Step 4:
81 goes into 209 2 times with a remainder of 47.
Use 2 as the next digit of our solution. 
Result so far: 62.0
If we subtract 162 from 209, we get 47.
Grab the next digit (0) from the dividend, add it to 47, then carry on: 470 / 81

Moving on to step 5:
81 can be fit into 470 5 times, resulting in a remainder of 65.
Put 5 as the next digit of the answer. 
Result so far: 625.0
The remainder is 65 after subtracting 405 from 470.
Fetch the next digit (5) from the dividend, attach it to 65 and continue: 655 / 81

Advancing to step 6:
When dividing 655 by 81, we get 8 with a remainder of 7.
The next digit of our result is 8. 
Result so far: 6258.0
The remainder is 7 after subtracting 648 from 655.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 7:
81 goes into 70 0 times with a remainder of 70.
Record the quotient 0 as the next digit in the result. 
Result so far: 6258.0
Subtracting 0 from 70 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 8:
If we divide 700 by 81, we get 8 and a remainder of 52.
The number 8 becomes the next digit in our result. 
Result so far: 6258.08
If we subtract 648 from 700, we 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.

Step 9:
If we divide 520 by 81, we get 6 and a remainder of 34.
Put 6 as the next digit of the answer. 
Result so far: 6258.086
If we take 486 away from 520, we end up with 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 10:
340 divided by 81 is 4 with a remainder of 16.
Write down 4 as next digit of the result. 
Result so far: 6258.0864
Deduct 324 from 340 and we're left 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.

Going ahead to step 11:
If we divide 160 by 81, we get 1 and a remainder of 79.
Write down 1 as next digit of the result. 
Result so far: 6258.08641
The remainder is 79 after subtracting 81 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

Let's proceed to step 12:
The number 81 fits into 790 9 times, leaving a remainder of 61.
Record the quotient 9 as the next digit in the result. 
Result so far: 6258.086419
Subtract 729 from 790 to get 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 13:
If we divide 610 by 81, we get 7 and a remainder of 43.
Write down 7 as next digit of the result. 
Result so far: 6258.0864197
The remainder is 43 after subtracting 567 from 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

On to step 14:
81 goes into 430 5 times with a remainder of 25.
The next digit of our result is 5. 
Result so far: 6258.08641975
If we take 405 away from 430, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The quotient of the division is 6258.08641975, and the remainder is 2.5e-08.