105052 ÷ 81 
The aim is to understand the frequency of 81 in 105052.

Step 1:
When dividing 1 by 81, we get 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 81

Step 2:
The number 81 fits into 10 0 times, leaving a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 81

Advancing to step 3:
81 goes into 105 1 times with a remainder of 24.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 81 from 105 to get 24.
Grab the next digit (0) from the dividend, add it to 24, then carry on: 240 / 81

On to step 4:
The number 81 fits into 240 2 times, leaving a remainder of 78.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Deduct 162 from 240 and we're left with 78.
Bring next digit (5) of the dividend behind the 78 and repeat the process: 785 / 81

Going ahead to step 5:
If we divide 785 by 81, we get 9 and a remainder of 56.
Write down 9 as next digit of the result. 
Result so far: 129.0
Subtract 729 from 785 to get 56.
Append the next digit (2) from the dividend to 56 and continue with: 562 / 81

Step 6:
When dividing 562 by 81, we get 6 with a remainder of 76.
Write down 6 as next digit of the result. 
Result so far: 1296.0
Deduct 486 from 562 and we're left with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Going ahead to step 7:
The number 81 fits into 760 9 times, leaving a remainder of 31.
Put 9 as the next digit of the answer. 
Result so far: 1296.9
Subtract 729 from 760 to get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 8:
When dividing 310 by 81, we get 3 with a remainder of 67.
Use 3 as the next digit of our solution. 
Result so far: 1296.93
Subtracting 243 from 310 leaves us with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Moving on to step 9:
The number 81 fits into 670 8 times, leaving a remainder of 22.
Use 8 as the next digit of our solution. 
Result so far: 1296.938
If we take 648 away from 670, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 10:
81 goes into 220 2 times with a remainder of 58.
Record the quotient 2 as the next digit in the result. 
Result so far: 1296.9382
Subtract 162 from 220 to get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Going ahead to step 11:
580 divided by 81 is 7 with a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 1296.93827
If we subtract 567 from 580, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 12:
When dividing 130 by 81, we get 1 with a remainder of 49.
The next digit of our result is 1. 
Result so far: 1296.938271
If we take 81 away from 130, we end up with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Step 13:
81 can be fit into 490 6 times, resulting in a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 1296.9382716
If we subtract 486 from 490, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 14:
The number 81 fits into 40 0 times, leaving a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 1296.9382716
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The final outcome is 1296.9382716, with a leftover of 4e-08.