We look at the division of 420634 by 77 
The aim is to understand the frequency of 77 in 420634.

Step 1:
77 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Include the next digit (2) from the dividend after 4, then repeat: 42 / 77

Going ahead to step 2:
When dividing 42 by 77, we get 0 with a remainder of 42.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Bring next digit (0) of the dividend behind the 42 and repeat the process: 420 / 77

Moving on to step 3:
420 divided by 77 is 5 with a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 5.0
The remainder is 35 after subtracting 385 from 420.
Include the next digit (6) from the dividend after 35, then repeat: 356 / 77

Step 4:
77 can be fit into 356 4 times, resulting in a remainder of 48.
Record the quotient 4 as the next digit in the result. 
Result so far: 54.0
If we take 308 away from 356, we end up with 48.
Include the next digit (3) from the dividend after 48, then repeat: 483 / 77

Let's proceed to step 5:
The number 77 fits into 483 6 times, leaving a remainder of 21.
Write down 6 as next digit of the result. 
Result so far: 546.0
The remainder is 21 after subtracting 462 from 483.
Grab the next digit (4) from the dividend, add it to 21, then carry on: 214 / 77

On to step 6:
If we divide 214 by 77, we get 2 and a remainder of 60.
The next digit of our result is 2. 
Result so far: 5462.0
If we take 154 away from 214, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 7:
77 can be fit into 600 7 times, resulting in a remainder of 61.
Record the quotient 7 as the next digit in the result. 
Result so far: 5462.7
Deduct 539 from 600 and we're left 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.

Going ahead to step 8:
The number 77 fits into 610 7 times, leaving a remainder of 71.
Put 7 as the next digit of the answer. 
Result so far: 5462.77
Subtract 539 from 610 to get 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

In conclusion, the division gives 5462.77 with a balance of 0.071.