66560690 ÷ 434 
The aim is to understand the frequency of 434 in 66560690.

Moving on to step 1:
When dividing 6 by 434, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (6) from the dividend, add it to 6, then carry on: 66 / 434

On to step 2:
66 divided by 434 is 0 with a remainder of 66.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 66, we get 66.
Include the next digit (5) from the dividend after 66, then repeat: 665 / 434

Advancing to step 3:
When dividing 665 by 434, we get 1 with a remainder of 231.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 434 from 665, we get 231.
Bring next digit (6) of the dividend behind the 231 and repeat the process: 2316 / 434

Step 4:
When dividing 2316 by 434, we get 5 with a remainder of 146.
Use 5 as the next digit of our solution. 
Result so far: 15.0
The remainder is 146 after subtracting 2170 from 2316.
Fetch the next digit (0) from the dividend, attach it to 146 and continue: 1460 / 434

On to step 5:
If we divide 1460 by 434, we get 3 and a remainder of 158.
The next digit of our result is 3. 
Result so far: 153.0
Deduct 1302 from 1460 and we're left with 158.
Grab the next digit (6) from the dividend, add it to 158, then carry on: 1586 / 434

On to step 6:
434 goes into 1586 3 times with a remainder of 284.
Use 3 as the next digit of our solution. 
Result so far: 1533.0
The remainder is 284 after subtracting 1302 from 1586.
Include the next digit (9) from the dividend after 284, then repeat: 2849 / 434

Let's proceed to step 7:
434 can be fit into 2849 6 times, resulting in a remainder of 245.
Record the quotient 6 as the next digit in the result. 
Result so far: 15336.0
Subtract 2604 from 2849 to get 245.
Append the next digit (0) from the dividend to 245 and continue with: 2450 / 434

On to step 8:
The number 434 fits into 2450 5 times, leaving a remainder of 280.
Record the quotient 5 as the next digit in the result. 
Result so far: 153365.0
Subtracting 2170 from 2450 leaves us with 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2800, and continue the process.

Advancing to step 9:
When dividing 2800 by 434, we get 6 with a remainder of 196.
Write down 6 as next digit of the result. 
Result so far: 153365.6
The remainder is 196 after subtracting 2604 from 2800.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1960, and continue the process.

Moving on to step 10:
When dividing 1960 by 434, we get 4 with a remainder of 224.
The next digit of our result is 4. 
Result so far: 153365.64
Deduct 1736 from 1960 and we're left with 224.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2240, and continue the process.

Advancing to step 11:
When dividing 2240 by 434, we get 5 with a remainder of 70.
The next digit of our result is 5. 
Result so far: 153365.645
Subtracting 2170 from 2240 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 12:
700 divided by 434 is 1 with a remainder of 266.
Use 1 as the next digit of our solution. 
Result so far: 153365.6451
If we take 434 away from 700, we end up with 266.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2660, and continue the process.

Advancing to step 13:
2660 divided by 434 is 6 with a remainder of 56.
Use 6 as the next digit of our solution. 
Result so far: 153365.64516
Subtracting 2604 from 2660 leaves us with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Advancing to step 14:
434 goes into 560 1 times with a remainder of 126.
The next digit of our result is 1. 
Result so far: 153365.645161
If we take 434 away from 560, we end up with 126.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1260, and continue the process.

Moving on to step 15:
434 can be fit into 1260 2 times, resulting in a remainder of 392.
Put 2 as the next digit of the answer. 
Result so far: 153365.6451612
Subtract 868 from 1260 to get 392.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3920, and continue the process.

On to step 16:
If we divide 3920 by 434, we get 9 and a remainder of 14.
The next digit of our result is 9. 
Result so far: 153365.64516129
Subtracting 3906 from 3920 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

In conclusion, the division gives 153365.64516129 with a balance of 1.4e-08.