Let's divide 71102601 by 686
The aim is to understand the frequency of 686 in 71102601.

Advancing to step 1:
When dividing 7 by 686, we get 0 with a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Include the next digit (1) from the dividend after 7, then repeat: 71 / 686

On to step 2:
When dividing 71 by 686, we get 0 with a remainder of 71.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 71 to get 71.
Grab the next digit (1) from the dividend, add it to 71, then carry on: 711 / 686

Let's proceed to step 3:
686 goes into 711 1 times with a remainder of 25.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 25 after subtracting 686 from 711.
Take the next digit (0) from the dividend and append it to 25, then repeat: 250 / 686

On to step 4:
The number 686 fits into 250 0 times, leaving a remainder of 250.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Subtracting 0 from 250 leaves us with 250.
Append the next digit (2) from the dividend to 250 and continue with: 2502 / 686

On to step 5:
686 can be fit into 2502 3 times, resulting in a remainder of 444.
Put 3 as the next digit of the answer. 
Result so far: 103.0
If we take 2058 away from 2502, we end up with 444.
Bring next digit (6) of the dividend behind the 444 and repeat the process: 4446 / 686

Step 6:
686 can be fit into 4446 6 times, resulting in a remainder of 330.
Write down 6 as next digit of the result. 
Result so far: 1036.0
Subtract 4116 from 4446 to get 330.
Include the next digit (0) from the dividend after 330, then repeat: 3300 / 686

Advancing to step 7:
686 can be fit into 3300 4 times, resulting in a remainder of 556.
The next digit of our result is 4. 
Result so far: 10364.0
If we take 2744 away from 3300, we end up with 556.
Take the next digit (1) from the dividend and append it to 556, then repeat: 5561 / 686

Going ahead to step 8:
686 can be fit into 5561 8 times, resulting in a remainder of 73.
Put 8 as the next digit of the answer. 
Result so far: 103648.0
Subtract 5488 from 5561 to get 73.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

Advancing to step 9:
730 divided by 686 is 1 with a remainder of 44.
Use 1 as the next digit of our solution. 
Result so far: 103648.1
Deduct 686 from 730 and we're left with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Let's proceed to step 10:
686 can be fit into 440 0 times, resulting in a remainder of 440.
Record the quotient 0 as the next digit in the result. 
Result so far: 103648.1
Subtracting 0 from 440 leaves us with 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4400, and continue the process.

Step 11:
4400 divided by 686 is 6 with a remainder of 284.
Use 6 as the next digit of our solution. 
Result so far: 103648.106
If we take 4116 away from 4400, we end up with 284.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2840, and continue the process.

Going ahead to step 12:
2840 divided by 686 is 4 with a remainder of 96.
Put 4 as the next digit of the answer. 
Result so far: 103648.1064
The remainder is 96 after subtracting 2744 from 2840.
Since there are no more digits in the dividend, we add a zero to the remainder making it 960, and continue the process.

Going ahead to step 13:
686 can be fit into 960 1 times, resulting in a remainder of 274.
The number 1 becomes the next digit in our result. 
Result so far: 103648.10641
The remainder is 274 after subtracting 686 from 960.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2740, and continue the process.

Advancing to step 14:
686 goes into 2740 3 times with a remainder of 682.
Put 3 as the next digit of the answer. 
Result so far: 103648.106413
Subtracting 2058 from 2740 leaves us with 682.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6820, and continue the process.

Advancing to step 15:
6820 divided by 686 is 9 with a remainder of 646.
The number 9 becomes the next digit in our result. 
Result so far: 103648.1064139
If we take 6174 away from 6820, we end up with 646.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6460, and continue the process.

Let's proceed to step 16:
If we divide 6460 by 686, we get 9 and a remainder of 286.
The number 9 becomes the next digit in our result. 
Result so far: 103648.10641399
If we subtract 6174 from 6460, we get 286.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2860, and continue the process.

In conclusion, the division gives 103648.10641399 with a balance of 2.86e-07.