We look at the division of 17419 by 42 
We want to figure out the number of times 17419 can be divided by 42.

Step 1:
When dividing 1 by 42, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 42

Going ahead to step 2:
42 can be fit into 17 0 times, resulting in a remainder of 17.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Take the next digit (4) from the dividend and append it to 17, then repeat: 174 / 42

On to step 3:
When dividing 174 by 42, we get 4 with a remainder of 6.
The next digit of our result is 4. 
Result so far: 4.0
The remainder is 6 after subtracting 168 from 174.
Append the next digit (1) from the dividend to 6 and continue with: 61 / 42

Moving on to step 4:
When dividing 61 by 42, we get 1 with a remainder of 19.
The number 1 becomes the next digit in our result. 
Result so far: 41.0
Subtracting 42 from 61 leaves us with 19.
Take the next digit (9) from the dividend and append it to 19, then repeat: 199 / 42

Advancing to step 5:
42 goes into 199 4 times with a remainder of 31.
The number 4 becomes the next digit in our result. 
Result so far: 414.0
Deduct 168 from 199 and we're left with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 6:
42 goes into 310 7 times with a remainder of 16.
Write down 7 as next digit of the result. 
Result so far: 414.7
The remainder is 16 after subtracting 294 from 310.
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 7:
42 goes into 160 3 times with a remainder of 34.
Write down 3 as next digit of the result. 
Result so far: 414.73
Deduct 126 from 160 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 8:
42 goes into 340 8 times with a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 414.738
If we subtract 336 from 340, 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.

On to step 9:
42 can be fit into 40 0 times, resulting in a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 414.738
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 10:
When dividing 400 by 42, we get 9 with a remainder of 22.
Put 9 as the next digit of the answer. 
Result so far: 414.73809
Subtract 378 from 400 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 11:
42 goes into 220 5 times with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 414.738095
Deduct 210 from 220 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.

Step 12:
100 divided by 42 is 2 with a remainder of 16.
The number 2 becomes the next digit in our result. 
Result so far: 414.7380952
Subtract 84 from 100 to 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.

Let's proceed to step 13:
The number 42 fits into 160 3 times, leaving a remainder of 34.
The number 3 becomes the next digit in our result. 
Result so far: 414.73809523
Subtracting 126 from 160 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

After the division, we end up with 414.73809523 and a remainder of 3.4e-08.