We're dividing 341035 by 42 
We want to divide 341035 by 42.

Let's proceed to step 1:
42 goes into 3 0 times with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 42

Moving on to step 2:
42 can be fit into 34 0 times, resulting in a remainder of 34.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 34, we end up with 34.
Grab the next digit (1) from the dividend, add it to 34, then carry on: 341 / 42

Step 3:
42 can be fit into 341 8 times, resulting in a remainder of 5.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we take 336 away from 341, we end up with 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 42

On to step 4:
42 can be fit into 50 1 times, resulting in a remainder of 8.
Write down 1 as next digit of the result. 
Result so far: 81.0
The remainder is 8 after subtracting 42 from 50.
Include the next digit (3) from the dividend after 8, then repeat: 83 / 42

On to step 5:
When dividing 83 by 42, we get 1 with a remainder of 41.
Use 1 as the next digit of our solution. 
Result so far: 811.0
Subtract 42 from 83 to get 41.
Bring next digit (5) of the dividend behind the 41 and repeat the process: 415 / 42

Advancing to step 6:
If we divide 415 by 42, we get 9 and a remainder of 37.
Write down 9 as next digit of the result. 
Result so far: 8119.0
If we take 378 away from 415, we end up with 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Let's proceed to step 7:
If we divide 370 by 42, we get 8 and a remainder of 34.
The next digit of our result is 8. 
Result so far: 8119.8
If we take 336 away from 370, 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.

Step 8:
340 divided by 42 is 8 with a remainder of 4.
The number 8 becomes the next digit in our result. 
Result so far: 8119.88
Subtract 336 from 340 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.

In conclusion, the division gives 8119.88 with a balance of 0.004.