We look at the division of 42510 by 19 
We want to figure out the number of times 42510 can be divided by 19.

Advancing to step 1:
19 can be fit into 4 0 times, resulting in a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 19

Moving on to step 2:
19 can be fit into 42 2 times, resulting in a remainder of 4.
Use 2 as the next digit of our solution. 
Result so far: 2.0
If we take 38 away from 42, we end up with 4.
Append the next digit (5) from the dividend to 4 and continue with: 45 / 19

Step 3:
19 can be fit into 45 2 times, resulting in a remainder of 7.
Use 2 as the next digit of our solution. 
Result so far: 22.0
The remainder is 7 after subtracting 38 from 45.
Append the next digit (1) from the dividend to 7 and continue with: 71 / 19

Moving on to step 4:
If we divide 71 by 19, we get 3 and a remainder of 14.
Use 3 as the next digit of our solution. 
Result so far: 223.0
If we subtract 57 from 71, we get 14.
Take the next digit (0) from the dividend and append it to 14, then repeat: 140 / 19

Going ahead to step 5:
When dividing 140 by 19, we get 7 with a remainder of 7.
Record the quotient 7 as the next digit in the result. 
Result so far: 2237.0
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 6:
If we divide 70 by 19, we get 3 and a remainder of 13.
The next digit of our result is 3. 
Result so far: 2237.3
Subtracting 57 from 70 leaves us 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.

On to step 7:
130 divided by 19 is 6 with a remainder of 16.
Write down 6 as next digit of the result. 
Result so far: 2237.36
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.

Moving on to step 8:
19 goes into 160 8 times with a remainder of 8.
The next digit of our result is 8. 
Result so far: 2237.368
The remainder is 8 after subtracting 152 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 9:
19 can be fit into 80 4 times, resulting in a remainder of 4.
The next digit of our result is 4. 
Result so far: 2237.3684
Subtract 76 from 80 to 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.

Let's proceed to step 10:
When dividing 40 by 19, we get 2 with a remainder of 2.
Write down 2 as next digit of the result. 
Result so far: 2237.36842
Subtract 38 from 40 to get 2.
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: 2237.368421
Deduct 19 from 20 and we're left 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.

Moving on to step 12:
When dividing 10 by 19, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 2237.368421
Deduct 0 from 10 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.

Going ahead to step 13:
The number 19 fits into 100 5 times, leaving a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 2237.36842105
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.

Our division results in 2237.36842105 with a remaining 5e-09.