105823 divided by 21 
We want to figure out the number of times 105823 can be divided by 21.

Going ahead to step 1:
21 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 21

Going ahead to step 2:
The number 21 fits into 10 0 times, leaving a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Take the next digit (5) from the dividend and append it to 10, then repeat: 105 / 21

Let's proceed to step 3:
105 divided by 21 is 5 with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtract 105 from 105 to get 0.
Grab the next digit (8) from the dividend, add it to 0, then carry on: 8 / 21

Let's proceed to step 4:
21 goes into 8 0 times with a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 50.0
If we subtract 0 from 8, we get 8.
Take the next digit (2) from the dividend and append it to 8, then repeat: 82 / 21

Advancing to step 5:
82 divided by 21 is 3 with a remainder of 19.
Record the quotient 3 as the next digit in the result. 
Result so far: 503.0
If we subtract 63 from 82, we get 19.
Append the next digit (3) from the dividend to 19 and continue with: 193 / 21

Advancing to step 6:
21 goes into 193 9 times with a remainder of 4.
The number 9 becomes the next digit in our result. 
Result so far: 5039.0
Subtract 189 from 193 to 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.

Step 7:
21 can be fit into 40 1 times, resulting in a remainder of 19.
The next digit of our result is 1. 
Result so far: 5039.1
Subtract 21 from 40 to get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 8:
The number 21 fits into 190 9 times, leaving a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 5039.19
Subtracting 189 from 190 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.

Let's proceed to step 9:
21 can be fit into 10 0 times, resulting in a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 5039.19
If we take 0 away from 10, 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.

Moving on to step 10:
When dividing 100 by 21, we get 4 with a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 5039.1904
If we subtract 84 from 100, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 11:
21 can be fit into 160 7 times, resulting in a remainder of 13.
Put 7 as the next digit of the answer. 
Result so far: 5039.19047
If we take 147 away from 160, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 12:
21 goes into 130 6 times with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 5039.190476
If we take 126 away from 130, we end up 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.

On to step 13:
The number 21 fits into 40 1 times, leaving a remainder of 19.
The next digit of our result is 1. 
Result so far: 5039.1904761
If we take 21 away from 40, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Going ahead to step 14:
21 can be fit into 190 9 times, resulting in a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 5039.19047619
Subtracting 189 from 190 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.

After the division, we end up with 5039.19047619 and a remainder of 1e-09.