341641 ÷ 11 
Our goal is to divide 341641 by 11.

Advancing to step 1:
When dividing 3 by 11, we get 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 11

Moving on to step 2:
34 divided by 11 is 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 3.0
If we take 33 away from 34, we end up with 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 11

Moving on to step 3:
11 divided by 11 is 1 with a remainder of 0.
The next digit of our result is 1. 
Result so far: 31.0
The remainder is 0 after subtracting 11 from 11.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 11

Let's proceed to step 4:
11 can be fit into 6 0 times, resulting in a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 310.0
Subtract 0 from 6 to get 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 11

Let's proceed to step 5:
If we divide 64 by 11, we get 5 and a remainder of 9.
Write down 5 as next digit of the result. 
Result so far: 3105.0
The remainder is 9 after subtracting 55 from 64.
Fetch the next digit (1) from the dividend, attach it to 9 and continue: 91 / 11

Advancing to step 6:
If we divide 91 by 11, we get 8 and a remainder of 3.
Write down 8 as next digit of the result. 
Result so far: 31058.0
Subtracting 88 from 91 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 7:
30 divided by 11 is 2 with a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 31058.2
Subtracting 22 from 30 leaves us 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.

On to step 8:
If we divide 80 by 11, we get 7 and a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 31058.27
Subtract 77 from 80 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 9:
The number 11 fits into 30 2 times, leaving a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 31058.272
Subtracting 22 from 30 leaves us 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.

Advancing to step 10:
If we divide 80 by 11, we get 7 and a remainder of 3.
Put 7 as the next digit of the answer. 
Result so far: 31058.2727
Subtract 77 from 80 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 11:
30 divided by 11 is 2 with a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 31058.27272
If we subtract 22 from 30, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 12:
If we divide 80 by 11, we get 7 and a remainder of 3.
The next digit of our result is 7. 
Result so far: 31058.272727
If we subtract 77 from 80, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 13:
When dividing 30 by 11, we get 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 31058.2727272
Deduct 22 from 30 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.

On to step 14:
The number 11 fits into 80 7 times, leaving a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 31058.27272727
Subtracting 77 from 80 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

After the division, we end up with 31058.27272727 and a remainder of 3e-09.