5665778 divided by 691 
The aim is to understand the frequency of 691 in 5665778.

Advancing to step 1:
If we divide 5 by 691, we get 0 and a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Fetch the next digit (6) from the dividend, attach it to 5 and continue: 56 / 691

Moving on to step 2:
The number 691 fits into 56 0 times, leaving a remainder of 56.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 56 and we're left with 56.
Grab the next digit (6) from the dividend, add it to 56, then carry on: 566 / 691

Advancing to step 3:
691 goes into 566 0 times with a remainder of 566.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 566 and we're left with 566.
Grab the next digit (5) from the dividend, add it to 566, then carry on: 5665 / 691

Let's proceed to step 4:
The number 691 fits into 5665 8 times, leaving a remainder of 137.
Write down 8 as next digit of the result. 
Result so far: 8.0
Subtracting 5528 from 5665 leaves us with 137.
Append the next digit (7) from the dividend to 137 and continue with: 1377 / 691

Going ahead to step 5:
The number 691 fits into 1377 1 times, leaving a remainder of 686.
The number 1 becomes the next digit in our result. 
Result so far: 81.0
If we take 691 away from 1377, we end up with 686.
Grab the next digit (7) from the dividend, add it to 686, then carry on: 6867 / 691

Advancing to step 6:
When dividing 6867 by 691, we get 9 with a remainder of 648.
The number 9 becomes the next digit in our result. 
Result so far: 819.0
Subtracting 6219 from 6867 leaves us with 648.
Append the next digit (8) from the dividend to 648 and continue with: 6488 / 691

On to step 7:
691 can be fit into 6488 9 times, resulting in a remainder of 269.
Write down 9 as next digit of the result. 
Result so far: 8199.0
If we subtract 6219 from 6488, we get 269.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2690, and continue the process.

Going ahead to step 8:
When dividing 2690 by 691, we get 3 with a remainder of 617.
The next digit of our result is 3. 
Result so far: 8199.3
Deduct 2073 from 2690 and we're left with 617.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6170, and continue the process.

Let's proceed to step 9:
6170 divided by 691 is 8 with a remainder of 642.
Put 8 as the next digit of the answer. 
Result so far: 8199.38
If we subtract 5528 from 6170, we get 642.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6420, and continue the process.

Advancing to step 10:
691 can be fit into 6420 9 times, resulting in a remainder of 201.
Put 9 as the next digit of the answer. 
Result so far: 8199.389
Subtracting 6219 from 6420 leaves us with 201.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2010, and continue the process.

Going ahead to step 11:
The number 691 fits into 2010 2 times, leaving a remainder of 628.
Write down 2 as next digit of the result. 
Result so far: 8199.3892
The remainder is 628 after subtracting 1382 from 2010.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6280, and continue the process.

Step 12:
691 can be fit into 6280 9 times, resulting in a remainder of 61.
Use 9 as the next digit of our solution. 
Result so far: 8199.38929
Subtracting 6219 from 6280 leaves us with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Let's proceed to step 13:
610 divided by 691 is 0 with a remainder of 610.
Use 0 as the next digit of our solution. 
Result so far: 8199.38929
Deduct 0 from 610 and we're left with 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6100, and continue the process.

Advancing to step 14:
691 can be fit into 6100 8 times, resulting in a remainder of 572.
Write down 8 as next digit of the result. 
Result so far: 8199.3892908
Subtracting 5528 from 6100 leaves us with 572.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5720, and continue the process.

Let's proceed to step 15:
The number 691 fits into 5720 8 times, leaving a remainder of 192.
The number 8 becomes the next digit in our result. 
Result so far: 8199.38929088
Subtracting 5528 from 5720 leaves us with 192.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1920, and continue the process.

The final outcome is 8199.38929088, with a leftover of 1.92e-07.