We look at the division of 157103 by 19 
The aim is to understand the frequency of 19 in 157103.

Advancing to step 1:
If we divide 1 by 19, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (5) from the dividend and append it to 1, then repeat: 15 / 19

On to step 2:
15 divided by 19 is 0 with a remainder of 15.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 15 and we're left with 15.
Include the next digit (7) from the dividend after 15, then repeat: 157 / 19

Let's proceed to step 3:
When dividing 157 by 19, we get 8 with a remainder of 5.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
If we subtract 152 from 157, we get 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 19

Moving on to step 4:
19 can be fit into 51 2 times, resulting in a remainder of 13.
The next digit of our result is 2. 
Result so far: 82.0
If we subtract 38 from 51, we get 13.
Grab the next digit (0) from the dividend, add it to 13, then carry on: 130 / 19

On to step 5:
The number 19 fits into 130 6 times, leaving a remainder of 16.
Use 6 as the next digit of our solution. 
Result so far: 826.0
Deduct 114 from 130 and we're left with 16.
Take the next digit (3) from the dividend and append it to 16, then repeat: 163 / 19

Step 6:
19 can be fit into 163 8 times, resulting in a remainder of 11.
Put 8 as the next digit of the answer. 
Result so far: 8268.0
The remainder is 11 after subtracting 152 from 163.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed 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: 8268.5
Subtract 95 from 110 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 8:
150 divided by 19 is 7 with a remainder of 17.
The number 7 becomes the next digit in our result. 
Result so far: 8268.57
Subtract 133 from 150 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Moving on to step 9:
When dividing 170 by 19, we get 8 with a remainder of 18.
Write down 8 as next digit of the result. 
Result so far: 8268.578
Subtract 152 from 170 to 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.

Going ahead to step 10:
When dividing 180 by 19, we get 9 with a remainder of 9.
The number 9 becomes the next digit in our result. 
Result so far: 8268.5789
If we take 171 away from 180, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 11:
19 goes into 90 4 times with a remainder of 14.
Put 4 as the next digit of the answer. 
Result so far: 8268.57894
If we take 76 away from 90, we end up 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.

Step 12:
The number 19 fits into 140 7 times, leaving a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 8268.578947
If we subtract 133 from 140, we 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.

Let's proceed to step 13:
When dividing 70 by 19, we get 3 with a remainder of 13.
Record the quotient 3 as the next digit in the result. 
Result so far: 8268.5789473
If we take 57 away from 70, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 14:
If we divide 130 by 19, we get 6 and a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 8268.57894736
Subtracting 114 from 130 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Our division results in 8268.57894736 with a remaining 1.6e-08.