171910 ÷ 21 
We want to figure out the number of times 171910 can be divided by 21.

Let's proceed to step 1:
When dividing 1 by 21, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 21

Advancing to step 2:
When dividing 17 by 21, we get 0 with a remainder of 17.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 17 to get 17.
Fetch the next digit (1) from the dividend, attach it to 17 and continue: 171 / 21

On to step 3:
When dividing 171 by 21, we get 8 with a remainder of 3.
Write down 8 as next digit of the result. 
Result so far: 8.0
If we take 168 away from 171, we end up with 3.
Take the next digit (9) from the dividend and append it to 3, then repeat: 39 / 21

Advancing to step 4:
When dividing 39 by 21, we get 1 with a remainder of 18.
Put 1 as the next digit of the answer. 
Result so far: 81.0
Subtract 21 from 39 to get 18.
Append the next digit (1) from the dividend to 18 and continue with: 181 / 21

On to step 5:
If we divide 181 by 21, we get 8 and a remainder of 13.
The number 8 becomes the next digit in our result. 
Result so far: 818.0
Subtract 168 from 181 to get 13.
Take the next digit (0) from the dividend and append it to 13, then repeat: 130 / 21

Moving on to step 6:
21 goes into 130 6 times with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 8186.0
The remainder is 4 after subtracting 126 from 130.
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 7:
21 goes into 40 1 times with a remainder of 19.
Use 1 as the next digit of our solution. 
Result so far: 8186.1
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 8:
21 goes into 190 9 times with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 8186.19
Deduct 189 from 190 and we're left 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.

On to step 9:
10 divided by 21 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 8186.19
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.

Advancing to step 10:
21 goes into 100 4 times with a remainder of 16.
Record the quotient 4 as the next digit in the result. 
Result so far: 8186.1904
Subtract 84 from 100 to 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.

Step 11:
The number 21 fits into 160 7 times, leaving a remainder of 13.
Put 7 as the next digit of the answer. 
Result so far: 8186.19047
If we subtract 147 from 160, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 12:
130 divided by 21 is 6 with a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 8186.190476
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:
21 goes into 40 1 times with a remainder of 19.
The number 1 becomes the next digit in our result. 
Result so far: 8186.1904761
If we subtract 21 from 40, we 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.

Going ahead to step 14:
The number 21 fits into 190 9 times, leaving a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 8186.19047619
If we take 189 away from 190, we end up 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 8186.19047619 and a remainder of 1e-09.