105719 divided by 21 
We want to figure out the number of times 105719 can be divided by 21.

Going ahead to step 1:
When dividing 1 by 21, we get 0 with a remainder of 1.
Write down 0 as next digit of 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

On to step 2:
21 can be fit into 10 0 times, resulting in a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 21

Step 3:
21 goes into 105 5 times with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 5.0
Deduct 105 from 105 and we're left with 0.
Take the next digit (7) from the dividend and append it to 0, then repeat: 7 / 21

Advancing to step 4:
When dividing 7 by 21, we get 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 50.0
If we take 0 away from 7, we end up with 7.
Include the next digit (1) from the dividend after 7, then repeat: 71 / 21

Let's proceed to step 5:
When dividing 71 by 21, we get 3 with a remainder of 8.
Put 3 as the next digit of the answer. 
Result so far: 503.0
If we take 63 away from 71, we end up with 8.
Take the next digit (9) from the dividend and append it to 8, then repeat: 89 / 21

Moving on to step 6:
When dividing 89 by 21, we get 4 with a remainder of 5.
Write down 4 as next digit of the result. 
Result so far: 5034.0
If we subtract 84 from 89, 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.

Advancing to step 7:
When dividing 50 by 21, we get 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 5034.2
Deduct 42 from 50 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 8:
80 divided by 21 is 3 with a remainder of 17.
Write down 3 as next digit of the result. 
Result so far: 5034.23
The remainder is 17 after subtracting 63 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 9:
The number 21 fits into 170 8 times, leaving a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 5034.238
Subtracting 168 from 170 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 10:
21 can be fit into 20 0 times, resulting in a remainder of 20.
The next digit of our result is 0. 
Result so far: 5034.238
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 11:
If we divide 200 by 21, we get 9 and a remainder of 11.
The number 9 becomes the next digit in our result. 
Result so far: 5034.23809
If we subtract 189 from 200, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 12:
21 can be fit into 110 5 times, resulting in a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 5034.238095
If we subtract 105 from 110, 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.

Step 13:
If we divide 50 by 21, we get 2 and a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 5034.2380952
If we take 42 away from 50, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 14:
80 divided by 21 is 3 with a remainder of 17.
The number 3 becomes the next digit in our result. 
Result so far: 5034.23809523
Deduct 63 from 80 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

After the division, we end up with 5034.23809523 and a remainder of 1.7e-08.