We're dividing 513742 by 77 
The aim is to understand the frequency of 77 in 513742.

Advancing to step 1:
77 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 77

On to step 2:
77 goes into 51 0 times with a remainder of 51.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Bring next digit (3) of the dividend behind the 51 and repeat the process: 513 / 77

Moving on to step 3:
The number 77 fits into 513 6 times, leaving a remainder of 51.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we take 462 away from 513, we end up with 51.
Grab the next digit (7) from the dividend, add it to 51, then carry on: 517 / 77

On to step 4:
77 goes into 517 6 times with a remainder of 55.
Use 6 as the next digit of our solution. 
Result so far: 66.0
Deduct 462 from 517 and we're left with 55.
Grab the next digit (4) from the dividend, add it to 55, then carry on: 554 / 77

Step 5:
The number 77 fits into 554 7 times, leaving a remainder of 15.
Write down 7 as next digit of the result. 
Result so far: 667.0
Subtract 539 from 554 to get 15.
Grab the next digit (2) from the dividend, add it to 15, then carry on: 152 / 77

On to step 6:
If we divide 152 by 77, we get 1 and a remainder of 75.
Use 1 as the next digit of our solution. 
Result so far: 6671.0
Subtract 77 from 152 to get 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

On to step 7:
When dividing 750 by 77, we get 9 with a remainder of 57.
Record the quotient 9 as the next digit in the result. 
Result so far: 6671.9
If we take 693 away from 750, we end up with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Advancing to step 8:
77 can be fit into 570 7 times, resulting in a remainder of 31.
The number 7 becomes the next digit in our result. 
Result so far: 6671.97
The remainder is 31 after subtracting 539 from 570.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

On to step 9:
If we divide 310 by 77, we get 4 and a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 6671.974
Deduct 308 from 310 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 10:
When dividing 20 by 77, we get 0 with a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 6671.974
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 11:
77 can be fit into 200 2 times, resulting in a remainder of 46.
The next digit of our result is 2. 
Result so far: 6671.97402
The remainder is 46 after subtracting 154 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Advancing to step 12:
77 goes into 460 5 times with a remainder of 75.
Put 5 as the next digit of the answer. 
Result so far: 6671.974025
If we take 385 away from 460, we end up with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Let's proceed to step 13:
The number 77 fits into 750 9 times, leaving a remainder of 57.
Use 9 as the next digit of our solution. 
Result so far: 6671.9740259
Subtracting 693 from 750 leaves us with 57.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Advancing to step 14:
77 can be fit into 570 7 times, resulting in a remainder of 31.
Record the quotient 7 as the next digit in the result. 
Result so far: 6671.97402597
The remainder is 31 after subtracting 539 from 570.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Our division results in 6671.97402597 with a remaining 3.1e-08.