We're dividing 181166 by 21 
The aim is to understand the frequency of 21 in 181166.

Advancing to step 1:
When dividing 1 by 21, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (8) from the dividend and append it to 1, then repeat: 18 / 21

Let's proceed to step 2:
21 goes into 18 0 times with a remainder of 18.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 18 and we're left with 18.
Fetch the next digit (1) from the dividend, attach it to 18 and continue: 181 / 21

Going ahead to step 3:
21 goes into 181 8 times with a remainder of 13.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Deduct 168 from 181 and we're left with 13.
Include the next digit (1) from the dividend after 13, then repeat: 131 / 21

Step 4:
21 goes into 131 6 times with a remainder of 5.
Write down 6 as next digit of the result. 
Result so far: 86.0
The remainder is 5 after subtracting 126 from 131.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 21

Step 5:
When dividing 56 by 21, we get 2 with a remainder of 14.
Use 2 as the next digit of our solution. 
Result so far: 862.0
If we subtract 42 from 56, we get 14.
Take the next digit (6) from the dividend and append it to 14, then repeat: 146 / 21

Advancing to step 6:
21 can be fit into 146 6 times, resulting in a remainder of 20.
Write down 6 as next digit of the result. 
Result so far: 8626.0
The remainder is 20 after subtracting 126 from 146.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 7:
The number 21 fits into 200 9 times, leaving a remainder of 11.
Put 9 as the next digit of the answer. 
Result so far: 8626.9
The remainder is 11 after subtracting 189 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 8:
21 goes into 110 5 times with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 8626.95
Deduct 105 from 110 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 9:
21 goes into 50 2 times with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 8626.952
If we take 42 away from 50, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 10:
21 goes into 80 3 times with a remainder of 17.
The number 3 becomes the next digit in our result. 
Result so far: 8626.9523
If we subtract 63 from 80, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Step 11:
The number 21 fits into 170 8 times, leaving a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 8626.95238
Deduct 168 from 170 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 12:
21 can be fit into 20 0 times, resulting in a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 8626.95238
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 13:
The number 21 fits into 200 9 times, leaving a remainder of 11.
The number 9 becomes the next digit in our result. 
Result so far: 8626.9523809
If we take 189 away from 200, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 14:
21 can be fit into 110 5 times, resulting in a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 8626.95238095
If we take 105 away from 110, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

After the division, we end up with 8626.95238095 and a remainder of 5e-09.