We look at the division of 106829 by 19 
The aim is to understand the frequency of 19 in 106829.

Advancing to step 1:
19 can be fit into 1 0 times, resulting in a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 19

On to step 2:
19 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 19

On to step 3:
106 divided by 19 is 5 with a remainder of 11.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Subtracting 95 from 106 leaves us with 11.
Bring next digit (8) of the dividend behind the 11 and repeat the process: 118 / 19

Moving on to step 4:
19 goes into 118 6 times with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 56.0
Deduct 114 from 118 and we're left with 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 19

On to step 5:
If we divide 42 by 19, we get 2 and a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 562.0
Subtracting 38 from 42 leaves us with 4.
Fetch the next digit (9) from the dividend, attach it to 4 and continue: 49 / 19

Let's proceed to step 6:
The number 19 fits into 49 2 times, leaving a remainder of 11.
Record the quotient 2 as the next digit in the result. 
Result so far: 5622.0
The remainder is 11 after subtracting 38 from 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 7:
If we divide 110 by 19, we get 5 and a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 5622.5
The remainder is 15 after subtracting 95 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 8:
When dividing 150 by 19, we get 7 with a remainder of 17.
Use 7 as the next digit of our solution. 
Result so far: 5622.57
Subtracting 133 from 150 leaves us with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 9:
The number 19 fits into 170 8 times, leaving a remainder of 18.
Write down 8 as next digit of the result. 
Result so far: 5622.578
If we take 152 away from 170, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 10:
19 goes into 180 9 times with a remainder of 9.
Write down 9 as next digit of the result. 
Result so far: 5622.5789
The remainder is 9 after subtracting 171 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Going ahead to step 11:
19 can be fit into 90 4 times, resulting in a remainder of 14.
Record the quotient 4 as the next digit in the result. 
Result so far: 5622.57894
Deduct 76 from 90 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 12:
The number 19 fits into 140 7 times, leaving a remainder of 7.
Put 7 as the next digit of the answer. 
Result so far: 5622.578947
Subtract 133 from 140 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Moving on to step 13:
70 divided by 19 is 3 with a remainder of 13.
The number 3 becomes the next digit in our result. 
Result so far: 5622.5789473
Subtract 57 from 70 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Let's proceed to step 14:
When dividing 130 by 19, we get 6 with a remainder of 16.
Record the quotient 6 as the next digit in the result. 
Result so far: 5622.57894736
If we subtract 114 from 130, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

After the division, we end up with 5622.57894736 and a remainder of 1.6e-08.