107729 divided by 71 
The aim is to understand the frequency of 71 in 107729.

Advancing to step 1:
If we divide 1 by 71, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 71

On to step 2:
If we divide 10 by 71, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Fetch the next digit (7) from the dividend, attach it to 10 and continue: 107 / 71

On to step 3:
107 divided by 71 is 1 with a remainder of 36.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 71 from 107, we get 36.
Fetch the next digit (7) from the dividend, attach it to 36 and continue: 367 / 71

Step 4:
The number 71 fits into 367 5 times, leaving a remainder of 12.
Write down 5 as next digit of the result. 
Result so far: 15.0
If we subtract 355 from 367, we get 12.
Grab the next digit (2) from the dividend, add it to 12, then carry on: 122 / 71

Going ahead to step 5:
71 can be fit into 122 1 times, resulting in a remainder of 51.
Put 1 as the next digit of the answer. 
Result so far: 151.0
If we take 71 away from 122, we end up with 51.
Take the next digit (9) from the dividend and append it to 51, then repeat: 519 / 71

Going ahead to step 6:
71 goes into 519 7 times with a remainder of 22.
Record the quotient 7 as the next digit in the result. 
Result so far: 1517.0
The remainder is 22 after subtracting 497 from 519.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 7:
When dividing 220 by 71, we get 3 with a remainder of 7.
Write down 3 as next digit of the result. 
Result so far: 1517.3
Subtracting 213 from 220 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 8:
The number 71 fits into 70 0 times, leaving a remainder of 70.
Write down 0 as next digit of the result. 
Result so far: 1517.3
Subtract 0 from 70 to get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 9:
71 goes into 700 9 times with a remainder of 61.
The next digit of our result is 9. 
Result so far: 1517.309
Subtract 639 from 700 to 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.

Let's proceed to step 10:
If we divide 610 by 71, we get 8 and a remainder of 42.
Put 8 as the next digit of the answer. 
Result so far: 1517.3098
If we subtract 568 from 610, we get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Moving on to step 11:
When dividing 420 by 71, we get 5 with a remainder of 65.
Use 5 as the next digit of our solution. 
Result so far: 1517.30985
The remainder is 65 after subtracting 355 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

On to step 12:
The number 71 fits into 650 9 times, leaving a remainder of 11.
Put 9 as the next digit of the answer. 
Result so far: 1517.309859
Subtract 639 from 650 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 13:
110 divided by 71 is 1 with a remainder of 39.
Use 1 as the next digit of our solution. 
Result so far: 1517.3098591
The remainder is 39 after subtracting 71 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Moving on to step 14:
71 can be fit into 390 5 times, resulting in a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 1517.30985915
Subtracting 355 from 390 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

After the division, we end up with 1517.30985915 and a remainder of 3.5e-08.