34401 ÷ 66 
The aim is to understand the frequency of 66 in 34401.

Let's proceed to step 1:
66 can be fit into 3 0 times, resulting in a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Grab the next digit (4) from the dividend, add it to 3, then carry on: 34 / 66

Moving on to step 2:
66 can be fit into 34 0 times, resulting in a remainder of 34.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 34 after subtracting 0 from 34.
Grab the next digit (4) from the dividend, add it to 34, then carry on: 344 / 66

Moving on to step 3:
344 divided by 66 is 5 with a remainder of 14.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Deduct 330 from 344 and we're left with 14.
Bring next digit (0) of the dividend behind the 14 and repeat the process: 140 / 66

Moving on to step 4:
66 goes into 140 2 times with a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 52.0
If we take 132 away from 140, we end up with 8.
Bring next digit (1) of the dividend behind the 8 and repeat the process: 81 / 66

Step 5:
81 divided by 66 is 1 with a remainder of 15.
The next digit of our result is 1. 
Result so far: 521.0
If we take 66 away from 81, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 6:
The number 66 fits into 150 2 times, leaving a remainder of 18.
The next digit of our result is 2. 
Result so far: 521.2
Subtracting 132 from 150 leaves us with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 7:
When dividing 180 by 66, we get 2 with a remainder of 48.
Record the quotient 2 as the next digit in the result. 
Result so far: 521.22
The remainder is 48 after subtracting 132 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

In conclusion, the division gives 521.22 with a balance of 0.048.