We divide 434161 by 42
We're looking to find how many times 42 goes into 434161.

Let's proceed to step 1:
The number 42 fits into 4 0 times, leaving a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 42

On to step 2:
If we divide 43 by 42, we get 1 and a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 42 from 43 and we're left with 1.
Take the next digit (4) from the dividend and append it to 1, then repeat: 14 / 42

Moving on to step 3:
If we divide 14 by 42, we get 0 and a remainder of 14.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
Deduct 0 from 14 and we're left with 14.
Fetch the next digit (1) from the dividend, attach it to 14 and continue: 141 / 42

Advancing to step 4:
If we divide 141 by 42, we get 3 and a remainder of 15.
Write down 3 as next digit of the result. 
Result so far: 103.0
Deduct 126 from 141 and we're left with 15.
Bring next digit (6) of the dividend behind the 15 and repeat the process: 156 / 42

Moving on to step 5:
When dividing 156 by 42, we get 3 with a remainder of 30.
Record the quotient 3 as the next digit in the result. 
Result so far: 1033.0
If we take 126 away from 156, we end up with 30.
Bring next digit (1) of the dividend behind the 30 and repeat the process: 301 / 42

Moving on to step 6:
42 can be fit into 301 7 times, resulting in a remainder of 7.
Use 7 as the next digit of our solution. 
Result so far: 10337.0
Subtracting 294 from 301 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 7:
70 divided by 42 is 1 with a remainder of 28.
Write down 1 as next digit of the result. 
Result so far: 10337.1
Subtracting 42 from 70 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 8:
If we divide 280 by 42, we get 6 and a remainder of 28.
The next digit of our result is 6. 
Result so far: 10337.16
Subtract 252 from 280 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 9:
The number 42 fits into 280 6 times, leaving a remainder of 28.
Put 6 as the next digit of the answer. 
Result so far: 10337.166
Subtract 252 from 280 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

In conclusion, the division gives 10337.166 with a balance of 0.0028.