257133 ÷ 81 
The aim is to understand the frequency of 81 in 257133.

Going ahead to step 1:
When dividing 2 by 81, we get 0 with a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 2, we end up with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 81

On to step 2:
The number 81 fits into 25 0 times, leaving a remainder of 25.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 25 to get 25.
Include the next digit (7) from the dividend after 25, then repeat: 257 / 81

Moving on to step 3:
257 divided by 81 is 3 with a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Subtracting 243 from 257 leaves us with 14.
Grab the next digit (1) from the dividend, add it to 14, then carry on: 141 / 81

Advancing to step 4:
The number 81 fits into 141 1 times, leaving a remainder of 60.
The next digit of our result is 1. 
Result so far: 31.0
Subtract 81 from 141 to get 60.
Fetch the next digit (3) from the dividend, attach it to 60 and continue: 603 / 81

Step 5:
When dividing 603 by 81, we get 7 with a remainder of 36.
Use 7 as the next digit of our solution. 
Result so far: 317.0
Subtracting 567 from 603 leaves us with 36.
Include the next digit (3) from the dividend after 36, then repeat: 363 / 81

Let's proceed to step 6:
The number 81 fits into 363 4 times, leaving a remainder of 39.
Put 4 as the next digit of the answer. 
Result so far: 3174.0
Subtract 324 from 363 to get 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Advancing to step 7:
81 can be fit into 390 4 times, resulting in a remainder of 66.
Record the quotient 4 as the next digit in the result. 
Result so far: 3174.4
The remainder is 66 after subtracting 324 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Going ahead to step 8:
81 can be fit into 660 8 times, resulting in a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 3174.48
Deduct 648 from 660 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 9:
The number 81 fits into 120 1 times, leaving a remainder of 39.
Use 1 as the next digit of our solution. 
Result so far: 3174.481
The remainder is 39 after subtracting 81 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

On to step 10:
The number 81 fits into 390 4 times, leaving a remainder of 66.
Put 4 as the next digit of the answer. 
Result so far: 3174.4814
The remainder is 66 after subtracting 324 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Advancing to step 11:
The number 81 fits into 660 8 times, leaving a remainder of 12.
Put 8 as the next digit of the answer. 
Result so far: 3174.48148
If we take 648 away from 660, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 12:
120 divided by 81 is 1 with a remainder of 39.
Write down 1 as next digit of the result. 
Result so far: 3174.481481
Deduct 81 from 120 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

On to step 13:
81 can be fit into 390 4 times, resulting in a remainder of 66.
The next digit of our result is 4. 
Result so far: 3174.4814814
Deduct 324 from 390 and we're left with 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Step 14:
660 divided by 81 is 8 with a remainder of 12.
The next digit of our result is 8. 
Result so far: 3174.48148148
Subtract 648 from 660 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

After the division, we end up with 3174.48148148 and a remainder of 1.2e-08.