We look at the division of 374598 by 19 
We want to figure out the number of times 374598 can be divided by 19.

Step 1:
If we divide 3 by 19, we get 0 and a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 19

On to step 2:
When dividing 37 by 19, we get 1 with a remainder of 18.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 19 from 37 to get 18.
Fetch the next digit (4) from the dividend, attach it to 18 and continue: 184 / 19

Step 3:
The number 19 fits into 184 9 times, leaving a remainder of 13.
Use 9 as the next digit of our solution. 
Result so far: 19.0
Deduct 171 from 184 and we're left with 13.
Take the next digit (5) from the dividend and append it to 13, then repeat: 135 / 19

On to step 4:
When dividing 135 by 19, we get 7 with a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 197.0
If we take 133 away from 135, we end up with 2.
Include the next digit (9) from the dividend after 2, then repeat: 29 / 19

Step 5:
If we divide 29 by 19, we get 1 and a remainder of 10.
Write down 1 as next digit of the result. 
Result so far: 1971.0
Subtracting 19 from 29 leaves us with 10.
Fetch the next digit (8) from the dividend, attach it to 10 and continue: 108 / 19

Let's proceed to step 6:
108 divided by 19 is 5 with a remainder of 13.
Put 5 as the next digit of the answer. 
Result so far: 19715.0
Subtract 95 from 108 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.

Advancing to step 7:
If we divide 130 by 19, we get 6 and a remainder of 16.
Use 6 as the next digit of our solution. 
Result so far: 19715.6
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.
Record the quotient 8 as the next digit in the result. 
Result so far: 19715.68
Subtract 152 from 160 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 9:
19 goes into 80 4 times with a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 19715.684
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.

Advancing to step 10:
19 can be fit into 40 2 times, resulting in a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 19715.6842
Subtracting 38 from 40 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 11:
19 goes into 20 1 times with a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 19715.68421
Subtract 19 from 20 to get 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.
Write down 0 as next digit of the result. 
Result so far: 19715.68421
If we take 0 away from 10, we end up 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.

Advancing to step 13:
19 goes into 100 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 19715.6842105
Deduct 95 from 100 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 14:
19 goes into 50 2 times with a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 19715.68421052
Subtract 38 from 50 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

After the division, we end up with 19715.68421052 and a remainder of 1.2e-08.