Let's divide 419305 by 42
We want to divide 419305 by 42.

Going ahead to step 1:
The number 42 fits into 4 0 times, leaving a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 42

Going ahead to step 2:
When dividing 41 by 42, we get 0 with a remainder of 41.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 41 leaves us with 41.
Take the next digit (9) from the dividend and append it to 41, then repeat: 419 / 42

Moving on to step 3:
42 goes into 419 9 times with a remainder of 41.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
Deduct 378 from 419 and we're left with 41.
Append the next digit (3) from the dividend to 41 and continue with: 413 / 42

Going ahead to step 4:
The number 42 fits into 413 9 times, leaving a remainder of 35.
The number 9 becomes the next digit in our result. 
Result so far: 99.0
If we subtract 378 from 413, we get 35.
Fetch the next digit (0) from the dividend, attach it to 35 and continue: 350 / 42

Moving on to step 5:
When dividing 350 by 42, we get 8 with a remainder of 14.
Use 8 as the next digit of our solution. 
Result so far: 998.0
Subtracting 336 from 350 leaves us with 14.
Grab the next digit (5) from the dividend, add it to 14, then carry on: 145 / 42

Going ahead to step 6:
145 divided by 42 is 3 with a remainder of 19.
Write down 3 as next digit of the result. 
Result so far: 9983.0
If we subtract 126 from 145, we get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 7:
42 goes into 190 4 times with a remainder of 22.
Put 4 as the next digit of the answer. 
Result so far: 9983.4
The remainder is 22 after subtracting 168 from 190.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 8:
42 goes into 220 5 times with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 9983.45
Subtracting 210 from 220 leaves us 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.

On to step 9:
The number 42 fits into 100 2 times, leaving a remainder of 16.
Record the quotient 2 as the next digit in the result. 
Result so far: 9983.452
If we subtract 84 from 100, 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.

Going ahead to step 10:
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: 9983.4523
If we take 126 away from 160, we end up 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.

On to step 11:
42 goes into 340 8 times with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 9983.45238
The remainder is 4 after subtracting 336 from 340.
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 12:
When dividing 40 by 42, we get 0 with a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 9983.45238
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 13:
400 divided by 42 is 9 with a remainder of 22.
The next digit of our result is 9. 
Result so far: 9983.4523809
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.

Advancing to step 14:
When dividing 220 by 42, we get 5 with a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 9983.45238095
If we subtract 210 from 220, 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.

In conclusion, the division gives 9983.45238095 with a balance of 1e-08.