175971 ÷ 21 
We're looking to find how many times 21 goes into 175971.

On to step 1:
21 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 21

Let's proceed to step 2:
21 goes into 17 0 times with a remainder of 17.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 17 to get 17.
Include the next digit (5) from the dividend after 17, then repeat: 175 / 21

Moving on to step 3:
21 can be fit into 175 8 times, resulting in a remainder of 7.
Use 8 as the next digit of our solution. 
Result so far: 8.0
Deduct 168 from 175 and we're left with 7.
Grab the next digit (9) from the dividend, add it to 7, then carry on: 79 / 21

Going ahead to step 4:
21 can be fit into 79 3 times, resulting in a remainder of 16.
Put 3 as the next digit of the answer. 
Result so far: 83.0
Subtracting 63 from 79 leaves us with 16.
Grab the next digit (7) from the dividend, add it to 16, then carry on: 167 / 21

Going ahead to step 5:
21 goes into 167 7 times with a remainder of 20.
Use 7 as the next digit of our solution. 
Result so far: 837.0
Subtracting 147 from 167 leaves us with 20.
Bring next digit (1) of the dividend behind the 20 and repeat the process: 201 / 21

Step 6:
21 goes into 201 9 times with a remainder of 12.
Record the quotient 9 as the next digit in the result. 
Result so far: 8379.0
Subtracting 189 from 201 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 7:
When dividing 120 by 21, we get 5 with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 8379.5
If we subtract 105 from 120, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 8:
When dividing 150 by 21, we get 7 with a remainder of 3.
Record the quotient 7 as the next digit in the result. 
Result so far: 8379.57
The remainder is 3 after subtracting 147 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 9:
When dividing 30 by 21, we get 1 with a remainder of 9.
The next digit of our result is 1. 
Result so far: 8379.571
If we subtract 21 from 30, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 10:
The number 21 fits into 90 4 times, leaving a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 8379.5714
Deduct 84 from 90 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.

On to step 11:
60 divided by 21 is 2 with a remainder of 18.
Write down 2 as next digit of the result. 
Result so far: 8379.57142
The remainder is 18 after subtracting 42 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Going ahead to step 12:
When dividing 180 by 21, we get 8 with a remainder of 12.
The next digit of our result is 8. 
Result so far: 8379.571428
If we subtract 168 from 180, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 13:
120 divided by 21 is 5 with a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 8379.5714285
Subtract 105 from 120 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 14:
150 divided by 21 is 7 with a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 8379.57142857
Subtract 147 from 150 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

In conclusion, the division gives 8379.57142857 with a balance of 3e-09.