We divide 586600 by 19
The aim is to understand the frequency of 19 in 586600.

On to step 1:
The number 19 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (8) from the dividend after 5, then repeat: 58 / 19

Advancing to step 2:
If we divide 58 by 19, we get 3 and a remainder of 1.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 1 after subtracting 57 from 58.
Include the next digit (6) from the dividend after 1, then repeat: 16 / 19

Moving on to step 3:
If we divide 16 by 19, we get 0 and a remainder of 16.
The next digit of our result is 0. 
Result so far: 30.0
Deduct 0 from 16 and we're left with 16.
Include the next digit (6) from the dividend after 16, then repeat: 166 / 19

Moving on to step 4:
19 goes into 166 8 times with a remainder of 14.
The next digit of our result is 8. 
Result so far: 308.0
Deduct 152 from 166 and we're left with 14.
Include the next digit (0) from the dividend after 14, then repeat: 140 / 19

Let's proceed to step 5:
19 can be fit into 140 7 times, resulting in a remainder of 7.
The next digit of our result is 7. 
Result so far: 3087.0
Subtracting 133 from 140 leaves us with 7.
Take the next digit (0) from the dividend and append it to 7, then repeat: 70 / 19

On to step 6:
If we divide 70 by 19, we get 3 and a remainder of 13.
Write down 3 as next digit of the result. 
Result so far: 30873.0
If we subtract 57 from 70, we 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.

Step 7:
130 divided by 19 is 6 with a remainder of 16.
The next digit of our result is 6. 
Result so far: 30873.6
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.

Moving on to step 8:
The number 19 fits into 160 8 times, leaving a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 30873.68
If we take 152 away from 160, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 9:
The number 19 fits into 80 4 times, leaving a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 30873.684
If we subtract 76 from 80, we 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.

Going ahead to step 10:
40 divided by 19 is 2 with a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 30873.6842
The remainder is 2 after subtracting 38 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 11:
19 goes into 20 1 times with a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 30873.68421
Subtracting 19 from 20 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 12:
10 divided by 19 is 0 with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 30873.68421
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 13:
The number 19 fits into 100 5 times, leaving a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 30873.6842105
The remainder is 5 after subtracting 95 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 14:
When dividing 50 by 19, we get 2 with a remainder of 12.
The number 2 becomes the next digit in our result. 
Result so far: 30873.68421052
Deduct 38 from 50 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final result is 30873.68421052 with a remainder of 1.2e-08.