533312 ÷ 41 
Our goal is to divide 533312 by 41.

Advancing to step 1:
When dividing 5 by 41, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Include the next digit (3) from the dividend after 5, then repeat: 53 / 41

Moving on to step 2:
41 can be fit into 53 1 times, resulting in a remainder of 12.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 41 from 53 leaves us with 12.
Append the next digit (3) from the dividend to 12 and continue with: 123 / 41

Moving on to step 3:
If we divide 123 by 41, we get 3 and a remainder of 0.
Record the quotient 3 as the next digit in the result. 
Result so far: 13.0
Subtract 123 from 123 to get 0.
Include the next digit (3) from the dividend after 0, then repeat: 3 / 41

Let's proceed to step 4:
If we divide 3 by 41, we get 0 and a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 130.0
Subtracting 0 from 3 leaves us with 3.
Append the next digit (1) from the dividend to 3 and continue with: 31 / 41

Advancing to step 5:
When dividing 31 by 41, we get 0 with a remainder of 31.
Put 0 as the next digit of the answer. 
Result so far: 1300.0
Deduct 0 from 31 and we're left with 31.
Fetch the next digit (2) from the dividend, attach it to 31 and continue: 312 / 41

Let's proceed to step 6:
312 divided by 41 is 7 with a remainder of 25.
Write down 7 as next digit of the result. 
Result so far: 13007.0
If we take 287 away from 312, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 7:
41 goes into 250 6 times with a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 13007.6
Deduct 246 from 250 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 8:
41 can be fit into 40 0 times, resulting in a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 13007.6
If we take 0 away from 40, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 9:
41 can be fit into 400 9 times, resulting in a remainder of 31.
Write down 9 as next digit of the result. 
Result so far: 13007.609
Deduct 369 from 400 and we're left with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 10:
When dividing 310 by 41, we get 7 with a remainder of 23.
The next digit of our result is 7. 
Result so far: 13007.6097
Subtract 287 from 310 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 11:
41 can be fit into 230 5 times, resulting in a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 13007.60975
The remainder is 25 after subtracting 205 from 230.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 12:
41 goes into 250 6 times with a remainder of 4.
Write down 6 as next digit of the result. 
Result so far: 13007.609756
If we subtract 246 from 250, we 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.

Going ahead to step 13:
41 goes into 40 0 times with a remainder of 40.
The next digit of our result is 0. 
Result so far: 13007.609756
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 14:
41 can be fit into 400 9 times, resulting in a remainder of 31.
Use 9 as the next digit of our solution. 
Result so far: 13007.60975609
The remainder is 31 after subtracting 369 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Our division results in 13007.60975609 with a remaining 3.1e-08.