We're dividing 176561 by 21 
Let's see how many times 21 fits into 176561.

Going ahead to step 1:
21 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 21

Going ahead to step 2:
If we divide 17 by 21, we get 0 and a remainder of 17.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 17, we end up with 17.
Append the next digit (6) from the dividend to 17 and continue with: 176 / 21

Let's proceed to step 3:
When dividing 176 by 21, we get 8 with a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
Subtracting 168 from 176 leaves us with 8.
Take the next digit (5) from the dividend and append it to 8, then repeat: 85 / 21

Advancing to step 4:
The number 21 fits into 85 4 times, leaving a remainder of 1.
Use 4 as the next digit of our solution. 
Result so far: 84.0
The remainder is 1 after subtracting 84 from 85.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 21

Step 5:
If we divide 16 by 21, we get 0 and a remainder of 16.
Use 0 as the next digit of our solution. 
Result so far: 840.0
If we take 0 away from 16, we end up with 16.
Fetch the next digit (1) from the dividend, attach it to 16 and continue: 161 / 21

On to step 6:
When dividing 161 by 21, we get 7 with a remainder of 14.
The number 7 becomes the next digit in our result. 
Result so far: 8407.0
If we take 147 away from 161, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
The number 21 fits into 140 6 times, leaving a remainder of 14.
Write down 6 as next digit of the result. 
Result so far: 8407.6
If we subtract 126 from 140, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

On to step 8:
The number 21 fits into 140 6 times, leaving a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 8407.66
Subtracting 126 from 140 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

The final result is 8407.66 with a remainder of 0.014.