16345 ÷ 41 
Our goal is to divide 16345 by 41.

Advancing to step 1:
If we divide 1 by 41, we get 0 and a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 41

Advancing to step 2:
16 divided by 41 is 0 with a remainder of 16.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 16 after subtracting 0 from 16.
Fetch the next digit (3) from the dividend, attach it to 16 and continue: 163 / 41

Moving on to step 3:
41 can be fit into 163 3 times, resulting in a remainder of 40.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Subtract 123 from 163 to get 40.
Include the next digit (4) from the dividend after 40, then repeat: 404 / 41

Let's proceed to step 4:
41 goes into 404 9 times with a remainder of 35.
Write down 9 as next digit of the result. 
Result so far: 39.0
Subtracting 369 from 404 leaves us with 35.
Take the next digit (5) from the dividend and append it to 35, then repeat: 355 / 41

Let's proceed to step 5:
If we divide 355 by 41, we get 8 and a remainder of 27.
The number 8 becomes the next digit in our result. 
Result so far: 398.0
Subtract 328 from 355 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Moving on to step 6:
270 divided by 41 is 6 with a remainder of 24.
The next digit of our result is 6. 
Result so far: 398.6
Deduct 246 from 270 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 7:
41 can be fit into 240 5 times, resulting in a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 398.65
Deduct 205 from 240 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 8:
350 divided by 41 is 8 with a remainder of 22.
The number 8 becomes the next digit in our result. 
Result so far: 398.658
Deduct 328 from 350 and we're left with 22.
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 9:
220 divided by 41 is 5 with a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 398.6585
If we subtract 205 from 220, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 10:
150 divided by 41 is 3 with a remainder of 27.
Write down 3 as next digit of the result. 
Result so far: 398.65853
Subtract 123 from 150 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 11:
270 divided by 41 is 6 with a remainder of 24.
Put 6 as the next digit of the answer. 
Result so far: 398.658536
The remainder is 24 after subtracting 246 from 270.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 12:
If we divide 240 by 41, we get 5 and a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 398.6585365
If we take 205 away from 240, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 13:
41 goes into 350 8 times with a remainder of 22.
Use 8 as the next digit of our solution. 
Result so far: 398.65853658
Subtract 328 from 350 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.

In conclusion, the division gives 398.65853658 with a balance of 2.2e-08.