81664561 ÷ 634 
The aim is to understand the frequency of 634 in 81664561.

Going ahead to step 1:
If we divide 8 by 634, we get 0 and a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 634

On to step 2:
81 divided by 634 is 0 with a remainder of 81.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 81 to get 81.
Append the next digit (6) from the dividend to 81 and continue with: 816 / 634

On to step 3:
If we divide 816 by 634, we get 1 and a remainder of 182.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 634 away from 816, we end up with 182.
Include the next digit (6) from the dividend after 182, then repeat: 1826 / 634

Let's proceed to step 4:
634 goes into 1826 2 times with a remainder of 558.
The next digit of our result is 2. 
Result so far: 12.0
The remainder is 558 after subtracting 1268 from 1826.
Fetch the next digit (4) from the dividend, attach it to 558 and continue: 5584 / 634

Going ahead to step 5:
When dividing 5584 by 634, we get 8 with a remainder of 512.
The number 8 becomes the next digit in our result. 
Result so far: 128.0
Subtracting 5072 from 5584 leaves us with 512.
Fetch the next digit (5) from the dividend, attach it to 512 and continue: 5125 / 634

On to step 6:
When dividing 5125 by 634, we get 8 with a remainder of 53.
Use 8 as the next digit of our solution. 
Result so far: 1288.0
If we subtract 5072 from 5125, we get 53.
Include the next digit (6) from the dividend after 53, then repeat: 536 / 634

Moving on to step 7:
536 divided by 634 is 0 with a remainder of 536.
The next digit of our result is 0. 
Result so far: 12880.0
The remainder is 536 after subtracting 0 from 536.
Grab the next digit (1) from the dividend, add it to 536, then carry on: 5361 / 634

Advancing to step 8:
634 can be fit into 5361 8 times, resulting in a remainder of 289.
Use 8 as the next digit of our solution. 
Result so far: 128808.0
If we take 5072 away from 5361, we end up with 289.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2890, and continue the process.

Moving on to step 9:
634 goes into 2890 4 times with a remainder of 354.
The next digit of our result is 4. 
Result so far: 128808.4
Subtract 2536 from 2890 to get 354.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3540, and continue the process.

Moving on to step 10:
634 goes into 3540 5 times with a remainder of 370.
The next digit of our result is 5. 
Result so far: 128808.45
Subtracting 3170 from 3540 leaves us with 370.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3700, and continue the process.

Moving on to step 11:
3700 divided by 634 is 5 with a remainder of 530.
The number 5 becomes the next digit in our result. 
Result so far: 128808.455
Deduct 3170 from 3700 and we're left with 530.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5300, and continue the process.

In conclusion, the division gives 128808.455 with a balance of 0.053.