We're dividing 421081 by 66 
We're looking to find how many times 66 goes into 421081.

On to step 1:
If we divide 4 by 66, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 66

Let's proceed to step 2:
When dividing 42 by 66, we get 0 with a remainder of 42.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 42, we end up with 42.
Append the next digit (1) from the dividend to 42 and continue with: 421 / 66

Advancing to step 3:
When dividing 421 by 66, we get 6 with a remainder of 25.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 25 after subtracting 396 from 421.
Fetch the next digit (0) from the dividend, attach it to 25 and continue: 250 / 66

Advancing to step 4:
When dividing 250 by 66, we get 3 with a remainder of 52.
Put 3 as the next digit of the answer. 
Result so far: 63.0
Subtract 198 from 250 to get 52.
Include the next digit (8) from the dividend after 52, then repeat: 528 / 66

On to step 5:
66 can be fit into 528 8 times, resulting in a remainder of 0.
The next digit of our result is 8. 
Result so far: 638.0
The remainder is 0 after subtracting 528 from 528.
Take the next digit (1) from the dividend and append it to 0, then repeat: 1 / 66

Advancing to step 6:
66 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 6380.0
Deduct 0 from 1 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.

Let's proceed to step 7:
When dividing 10 by 66, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 6380.0
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 8:
66 can be fit into 100 1 times, resulting in a remainder of 34.
Record the quotient 1 as the next digit in the result. 
Result so far: 6380.01
Subtract 66 from 100 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 9:
340 divided by 66 is 5 with a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 6380.015
If we subtract 330 from 340, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 10:
The number 66 fits into 100 1 times, leaving a remainder of 34.
Write down 1 as next digit of the result. 
Result so far: 6380.0151
If we take 66 away from 100, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 11:
66 can be fit into 340 5 times, resulting in a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 6380.01515
Subtract 330 from 340 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 12:
66 can be fit into 100 1 times, resulting in a remainder of 34.
The number 1 becomes the next digit in our result. 
Result so far: 6380.015151
Subtracting 66 from 100 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Going ahead to step 13:
340 divided by 66 is 5 with a remainder of 10.
The number 5 becomes the next digit in our result. 
Result so far: 6380.0151515
Subtracting 330 from 340 leaves us 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.

Let's proceed to step 14:
The number 66 fits into 100 1 times, leaving a remainder of 34.
Record the quotient 1 as the next digit in the result. 
Result so far: 6380.01515151
Subtract 66 from 100 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

After the division, we end up with 6380.01515151 and a remainder of 3.4e-08.