43231781 ÷ 665 
The aim is to understand the frequency of 665 in 43231781.

Let's proceed to step 1:
When dividing 4 by 665, we get 0 with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 665

Advancing to step 2:
665 can be fit into 43 0 times, resulting in a remainder of 43.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 43 after subtracting 0 from 43.
Fetch the next digit (2) from the dividend, attach it to 43 and continue: 432 / 665

Let's proceed to step 3:
665 can be fit into 432 0 times, resulting in a remainder of 432.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 432 after subtracting 0 from 432.
Include the next digit (3) from the dividend after 432, then repeat: 4323 / 665

Going ahead to step 4:
The number 665 fits into 4323 6 times, leaving a remainder of 333.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Deduct 3990 from 4323 and we're left with 333.
Append the next digit (1) from the dividend to 333 and continue with: 3331 / 665

Going ahead to step 5:
When dividing 3331 by 665, we get 5 with a remainder of 6.
The next digit of our result is 5. 
Result so far: 65.0
If we subtract 3325 from 3331, we get 6.
Include the next digit (7) from the dividend after 6, then repeat: 67 / 665

Step 6:
When dividing 67 by 665, we get 0 with a remainder of 67.
Use 0 as the next digit of our solution. 
Result so far: 650.0
Subtracting 0 from 67 leaves us with 67.
Append the next digit (8) from the dividend to 67 and continue with: 678 / 665

Step 7:
665 goes into 678 1 times with a remainder of 13.
The next digit of our result is 1. 
Result so far: 6501.0
If we subtract 665 from 678, we get 13.
Bring next digit (1) of the dividend behind the 13 and repeat the process: 131 / 665

Moving on to step 8:
The number 665 fits into 131 0 times, leaving a remainder of 131.
Use 0 as the next digit of our solution. 
Result so far: 65010.0
Subtracting 0 from 131 leaves us with 131.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1310, and continue the process.

Step 9:
665 can be fit into 1310 1 times, resulting in a remainder of 645.
The number 1 becomes the next digit in our result. 
Result so far: 65010.1
If we take 665 away from 1310, we end up with 645.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6450, and continue the process.

Let's proceed to step 10:
When dividing 6450 by 665, we get 9 with a remainder of 465.
Use 9 as the next digit of our solution. 
Result so far: 65010.19
If we subtract 5985 from 6450, we get 465.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4650, and continue the process.

Going ahead to step 11:
4650 divided by 665 is 6 with a remainder of 660.
Put 6 as the next digit of the answer. 
Result so far: 65010.196
The remainder is 660 after subtracting 3990 from 4650.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6600, and continue the process.

Let's proceed to step 12:
When dividing 6600 by 665, we get 9 with a remainder of 615.
Put 9 as the next digit of the answer. 
Result so far: 65010.1969
Subtract 5985 from 6600 to get 615.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6150, and continue the process.

Advancing to step 13:
If we divide 6150 by 665, we get 9 and a remainder of 165.
Write down 9 as next digit of the result. 
Result so far: 65010.19699
If we take 5985 away from 6150, we end up with 165.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1650, and continue the process.

In conclusion, the division gives 65010.19699 with a balance of 0.000165.