We look at the division of 105582 by 96 
We're looking to find how many times 96 goes into 105582.

Going ahead to step 1:
96 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 96

Let's proceed to step 2:
96 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 96

Let's proceed to step 3:
The number 96 fits into 105 1 times, leaving a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 96 from 105 and we're left with 9.
Include the next digit (5) from the dividend after 9, then repeat: 95 / 96

Step 4:
96 goes into 95 0 times with a remainder of 95.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Deduct 0 from 95 and we're left with 95.
Bring next digit (8) of the dividend behind the 95 and repeat the process: 958 / 96

Moving on to step 5:
96 goes into 958 9 times with a remainder of 94.
Put 9 as the next digit of the answer. 
Result so far: 109.0
Subtract 864 from 958 to get 94.
Bring next digit (2) of the dividend behind the 94 and repeat the process: 942 / 96

Step 6:
942 divided by 96 is 9 with a remainder of 78.
The next digit of our result is 9. 
Result so far: 1099.0
The remainder is 78 after subtracting 864 from 942.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

On to step 7:
780 divided by 96 is 8 with a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 1099.8
The remainder is 12 after subtracting 768 from 780.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 8:
96 goes into 120 1 times with a remainder of 24.
Use 1 as the next digit of our solution. 
Result so far: 1099.81
If we take 96 away from 120, we end up 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.

Advancing to step 9:
96 goes into 240 2 times with a remainder of 48.
Use 2 as the next digit of our solution. 
Result so far: 1099.812
If we take 192 away from 240, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 10:
480 divided by 96 is 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 1099.8125
Deduct 480 from 480 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Moving on to step 11:
96 goes into 0 0 times with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 1099.8125
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 12:
96 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 1099.8125
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 1099.8125 with a balance of 0.0.