127117 divided by 34 
The aim is to understand the frequency of 34 in 127117.

On to step 1:
When dividing 1 by 34, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 34

Moving on to step 2:
34 goes into 12 0 times with a remainder of 12.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 12 leaves us with 12.
Include the next digit (7) from the dividend after 12, then repeat: 127 / 34

On to step 3:
34 can be fit into 127 3 times, resulting in a remainder of 25.
The next digit of our result is 3. 
Result so far: 3.0
Deduct 102 from 127 and we're left with 25.
Include the next digit (1) from the dividend after 25, then repeat: 251 / 34

Advancing to step 4:
If we divide 251 by 34, we get 7 and a remainder of 13.
The next digit of our result is 7. 
Result so far: 37.0
Subtract 238 from 251 to get 13.
Bring next digit (1) of the dividend behind the 13 and repeat the process: 131 / 34

Advancing to step 5:
If we divide 131 by 34, we get 3 and a remainder of 29.
The next digit of our result is 3. 
Result so far: 373.0
Deduct 102 from 131 and we're left with 29.
Append the next digit (7) from the dividend to 29 and continue with: 297 / 34

Going ahead to step 6:
297 divided by 34 is 8 with a remainder of 25.
Record the quotient 8 as the next digit in the result. 
Result so far: 3738.0
Deduct 272 from 297 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 7:
If we divide 250 by 34, we get 7 and a remainder of 12.
Write down 7 as next digit of the result. 
Result so far: 3738.7
The remainder is 12 after subtracting 238 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 8:
34 goes into 120 3 times with a remainder of 18.
Use 3 as the next digit of our solution. 
Result so far: 3738.73
If we subtract 102 from 120, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 9:
If we divide 180 by 34, we get 5 and a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 3738.735
Deduct 170 from 180 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 10:
When dividing 100 by 34, we get 2 with a remainder of 32.
The number 2 becomes the next digit in our result. 
Result so far: 3738.7352
Subtract 68 from 100 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 11:
The number 34 fits into 320 9 times, leaving a remainder of 14.
The next digit of our result is 9. 
Result so far: 3738.73529
Subtract 306 from 320 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 12:
When dividing 140 by 34, we get 4 with a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 3738.735294
Subtract 136 from 140 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 13:
The number 34 fits into 40 1 times, leaving a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 3738.7352941
If we take 34 away from 40, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 14:
If we divide 60 by 34, we get 1 and a remainder of 26.
The next digit of our result is 1. 
Result so far: 3738.73529411
Subtracting 34 from 60 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

The final result is 3738.73529411 with a remainder of 2.6e-08.