We're dividing 341645 by 42 
We're looking to find how many times 42 goes into 341645.

On to step 1:
42 can be fit into 3 0 times, resulting in a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Fetch the next digit (4) from the dividend, attach it to 3 and continue: 34 / 42

On to step 2:
The number 42 fits into 34 0 times, leaving a remainder of 34.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 34 and we're left with 34.
Grab the next digit (1) from the dividend, add it to 34, then carry on: 341 / 42

Moving on to step 3:
42 can be fit into 341 8 times, resulting in a remainder of 5.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
If we take 336 away from 341, we end up with 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 42

Going ahead to step 4:
When dividing 56 by 42, we get 1 with a remainder of 14.
The number 1 becomes the next digit in our result. 
Result so far: 81.0
If we take 42 away from 56, we end up with 14.
Include the next digit (4) from the dividend after 14, then repeat: 144 / 42

On to step 5:
42 goes into 144 3 times with a remainder of 18.
Record the quotient 3 as the next digit in the result. 
Result so far: 813.0
If we subtract 126 from 144, we get 18.
Fetch the next digit (5) from the dividend, attach it to 18 and continue: 185 / 42

Moving on to step 6:
42 can be fit into 185 4 times, resulting in a remainder of 17.
The number 4 becomes the next digit in our result. 
Result so far: 8134.0
If we take 168 away from 185, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 7:
170 divided by 42 is 4 with a remainder of 2.
The next digit of our result is 4. 
Result so far: 8134.4
If we subtract 168 from 170, we 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.

Step 8:
42 can be fit into 20 0 times, resulting in a remainder of 20.
The next digit of our result is 0. 
Result so far: 8134.4
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 9:
The number 42 fits into 200 4 times, leaving a remainder of 32.
Write down 4 as next digit of the result. 
Result so far: 8134.404
If we subtract 168 from 200, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 10:
When dividing 320 by 42, we get 7 with a remainder of 26.
The number 7 becomes the next digit in our result. 
Result so far: 8134.4047
Subtracting 294 from 320 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 11:
260 divided by 42 is 6 with a remainder of 8.
Write down 6 as next digit of the result. 
Result so far: 8134.40476
Deduct 252 from 260 and we're left with 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 12:
42 can be fit into 80 1 times, resulting in a remainder of 38.
Record the quotient 1 as the next digit in the result. 
Result so far: 8134.404761
If we take 42 away from 80, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

On to step 13:
42 can be fit into 380 9 times, resulting in a remainder of 2.
The number 9 becomes the next digit in our result. 
Result so far: 8134.4047619
If we subtract 378 from 380, we 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.

Let's proceed to step 14:
When dividing 20 by 42, we get 0 with a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 8134.4047619
If we subtract 0 from 20, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

In conclusion, the division gives 8134.4047619 with a balance of 2e-08.