We look at the division of 77725706 by 643 
The aim is to understand the frequency of 643 in 77725706.

Advancing to step 1:
If we divide 7 by 643, we get 0 and a remainder of 7.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Grab the next digit (7) from the dividend, add it to 7, then carry on: 77 / 643

Advancing to step 2:
If we divide 77 by 643, we get 0 and a remainder of 77.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 77 to get 77.
Fetch the next digit (7) from the dividend, attach it to 77 and continue: 777 / 643

Advancing to step 3:
643 can be fit into 777 1 times, resulting in a remainder of 134.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 643 from 777 and we're left with 134.
Fetch the next digit (2) from the dividend, attach it to 134 and continue: 1342 / 643

Advancing to step 4:
643 goes into 1342 2 times with a remainder of 56.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
If we subtract 1286 from 1342, we get 56.
Fetch the next digit (5) from the dividend, attach it to 56 and continue: 565 / 643

Moving on to step 5:
The number 643 fits into 565 0 times, leaving a remainder of 565.
Write down 0 as next digit of the result. 
Result so far: 120.0
If we subtract 0 from 565, we get 565.
Fetch the next digit (7) from the dividend, attach it to 565 and continue: 5657 / 643

Step 6:
5657 divided by 643 is 8 with a remainder of 513.
Put 8 as the next digit of the answer. 
Result so far: 1208.0
Subtracting 5144 from 5657 leaves us with 513.
Grab the next digit (0) from the dividend, add it to 513, then carry on: 5130 / 643

Let's proceed to step 7:
When dividing 5130 by 643, we get 7 with a remainder of 629.
The next digit of our result is 7. 
Result so far: 12087.0
Subtracting 4501 from 5130 leaves us with 629.
Fetch the next digit (6) from the dividend, attach it to 629 and continue: 6296 / 643

Step 8:
If we divide 6296 by 643, we get 9 and a remainder of 509.
The next digit of our result is 9. 
Result so far: 120879.0
Deduct 5787 from 6296 and we're left with 509.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5090, and continue the process.

Going ahead to step 9:
The number 643 fits into 5090 7 times, leaving a remainder of 589.
Put 7 as the next digit of the answer. 
Result so far: 120879.7
The remainder is 589 after subtracting 4501 from 5090.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5890, and continue the process.

Let's proceed to step 10:
5890 divided by 643 is 9 with a remainder of 103.
Put 9 as the next digit of the answer. 
Result so far: 120879.79
The remainder is 103 after subtracting 5787 from 5890.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1030, and continue the process.

On to step 11:
If we divide 1030 by 643, we get 1 and a remainder of 387.
The next digit of our result is 1. 
Result so far: 120879.791
If we take 643 away from 1030, we end up with 387.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3870, and continue the process.

On to step 12:
When dividing 3870 by 643, we get 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 120879.7916
Subtract 3858 from 3870 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 13:
643 goes into 120 0 times with a remainder of 120.
The number 0 becomes the next digit in our result. 
Result so far: 120879.7916
Subtracting 0 from 120 leaves us with 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1200, and continue the process.

On to step 14:
If we divide 1200 by 643, we get 1 and a remainder of 557.
Use 1 as the next digit of our solution. 
Result so far: 120879.791601
The remainder is 557 after subtracting 643 from 1200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5570, and continue the process.

Advancing to step 15:
If we divide 5570 by 643, we get 8 and a remainder of 426.
Use 8 as the next digit of our solution. 
Result so far: 120879.7916018
If we subtract 5144 from 5570, we get 426.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4260, and continue the process.

Step 16:
643 goes into 4260 6 times with a remainder of 402.
The next digit of our result is 6. 
Result so far: 120879.79160186
Subtract 3858 from 4260 to get 402.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4020, and continue the process.

In conclusion, the division gives 120879.79160186 with a balance of 4.02e-07.