581641 ÷ 77 
The aim is to understand the frequency of 77 in 581641.

Let's proceed to step 1:
77 can be fit into 5 0 times, resulting in a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 77

On to step 2:
If we divide 58 by 77, we get 0 and a remainder of 58.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 58 leaves us with 58.
Include the next digit (1) from the dividend after 58, then repeat: 581 / 77

Step 3:
When dividing 581 by 77, we get 7 with a remainder of 42.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtracting 539 from 581 leaves us with 42.
Append the next digit (6) from the dividend to 42 and continue with: 426 / 77

Going ahead to step 4:
77 goes into 426 5 times with a remainder of 41.
Record the quotient 5 as the next digit in the result. 
Result so far: 75.0
If we take 385 away from 426, we end up with 41.
Include the next digit (4) from the dividend after 41, then repeat: 414 / 77

Moving on to step 5:
The number 77 fits into 414 5 times, leaving a remainder of 29.
Put 5 as the next digit of the answer. 
Result so far: 755.0
If we take 385 away from 414, we end up with 29.
Grab the next digit (1) from the dividend, add it to 29, then carry on: 291 / 77

Step 6:
When dividing 291 by 77, we get 3 with a remainder of 60.
Use 3 as the next digit of our solution. 
Result so far: 7553.0
The remainder is 60 after subtracting 231 from 291.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 7:
The number 77 fits into 600 7 times, leaving a remainder of 61.
Put 7 as the next digit of the answer. 
Result so far: 7553.7
If we subtract 539 from 600, we get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Step 8:
610 divided by 77 is 7 with a remainder of 71.
Put 7 as the next digit of the answer. 
Result so far: 7553.77
Deduct 539 from 610 and we're left with 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

The final result is 7553.77 with a remainder of 0.071.