105826 ÷ 11 
We want to figure out the number of times 105826 can be divided by 11.

Moving on to step 1:
When dividing 1 by 11, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 11

Moving on to step 2:
11 can be fit into 10 0 times, resulting in a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 11

Let's proceed to step 3:
When dividing 105 by 11, we get 9 with a remainder of 6.
Put 9 as the next digit of the answer. 
Result so far: 9.0
Subtracting 99 from 105 leaves us with 6.
Fetch the next digit (8) from the dividend, attach it to 6 and continue: 68 / 11

Moving on to step 4:
68 divided by 11 is 6 with a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 96.0
Subtracting 66 from 68 leaves us with 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 11

On to step 5:
If we divide 22 by 11, we get 2 and a remainder of 0.
Put 2 as the next digit of the answer. 
Result so far: 962.0
Deduct 22 from 22 and we're left with 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 11

On to step 6:
When dividing 6 by 11, we get 0 with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 9620.0
Subtract 0 from 6 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 7:
11 can be fit into 60 5 times, resulting in a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 9620.5
If we subtract 55 from 60, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
If we divide 50 by 11, we get 4 and a remainder of 6.
Record the quotient 4 as the next digit in the result. 
Result so far: 9620.54
Deduct 44 from 50 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 9:
11 goes into 60 5 times with a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 9620.545
If we subtract 55 from 60, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 10:
When dividing 50 by 11, we get 4 with a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 9620.5454
Subtract 44 from 50 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 11:
When dividing 60 by 11, we get 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 9620.54545
Subtracting 55 from 60 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 12:
When dividing 50 by 11, we get 4 with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 9620.545454
If we take 44 away from 50, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 13:
11 goes into 60 5 times with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 9620.5454545
If we take 55 away from 60, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 14:
The number 11 fits into 50 4 times, leaving a remainder of 6.
Put 4 as the next digit of the answer. 
Result so far: 9620.54545454
If we subtract 44 from 50, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 9620.54545454 and a remainder of 6e-09.