Let's divide 41584 by 13
We want to divide 41584 by 13.

Step 1:
When dividing 4 by 13, we get 0 with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 13

Going ahead to step 2:
The number 13 fits into 41 3 times, leaving a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Subtract 39 from 41 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 13

On to step 3:
If we divide 25 by 13, we get 1 and a remainder of 12.
Put 1 as the next digit of the answer. 
Result so far: 31.0
If we take 13 away from 25, we end up with 12.
Take the next digit (8) from the dividend and append it to 12, then repeat: 128 / 13

Going ahead to step 4:
128 divided by 13 is 9 with a remainder of 11.
The next digit of our result is 9. 
Result so far: 319.0
Deduct 117 from 128 and we're left with 11.
Grab the next digit (4) from the dividend, add it to 11, then carry on: 114 / 13

Step 5:
The number 13 fits into 114 8 times, leaving a remainder of 10.
The next digit of our result is 8. 
Result so far: 3198.0
If we take 104 away from 114, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 6:
If we divide 100 by 13, we get 7 and a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 3198.7
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 7:
90 divided by 13 is 6 with a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 3198.76
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 8:
The number 13 fits into 120 9 times, leaving a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 3198.769
If we take 117 away from 120, we end up 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.

Advancing to step 9:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 3198.7692
Subtracting 26 from 30 leaves us 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.

Let's proceed to step 10:
The number 13 fits into 40 3 times, leaving a remainder of 1.
The next digit of our result is 3. 
Result so far: 3198.76923
Subtracting 39 from 40 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 11:
When dividing 10 by 13, we get 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 3198.76923
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 12:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Write down 7 as next digit of the result. 
Result so far: 3198.7692307
Deduct 91 from 100 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 13:
13 can be fit into 90 6 times, resulting in a remainder of 12.
Record the quotient 6 as the next digit in the result. 
Result so far: 3198.76923076
The remainder is 12 after subtracting 78 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 3198.76923076 with a balance of 1.2e-08.