205665 ÷ 66 
Our goal is to divide 205665 by 66.

Advancing to step 1:
The number 66 fits into 2 0 times, leaving a remainder of 2.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Grab the next digit (0) from the dividend, add it to 2, then carry on: 20 / 66

Moving on to step 2:
The number 66 fits into 20 0 times, leaving a remainder of 20.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 20, we end up with 20.
Append the next digit (5) from the dividend to 20 and continue with: 205 / 66

Moving on to step 3:
When dividing 205 by 66, we get 3 with a remainder of 7.
The next digit of our result is 3. 
Result so far: 3.0
The remainder is 7 after subtracting 198 from 205.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 66

Let's proceed to step 4:
If we divide 76 by 66, we get 1 and a remainder of 10.
The number 1 becomes the next digit in our result. 
Result so far: 31.0
If we take 66 away from 76, we end up with 10.
Append the next digit (6) from the dividend to 10 and continue with: 106 / 66

Advancing to step 5:
If we divide 106 by 66, we get 1 and a remainder of 40.
The number 1 becomes the next digit in our result. 
Result so far: 311.0
Subtracting 66 from 106 leaves us with 40.
Bring next digit (5) of the dividend behind the 40 and repeat the process: 405 / 66

Step 6:
405 divided by 66 is 6 with a remainder of 9.
Use 6 as the next digit of our solution. 
Result so far: 3116.0
Subtracting 396 from 405 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 7:
The number 66 fits into 90 1 times, leaving a remainder of 24.
Put 1 as the next digit of the answer. 
Result so far: 3116.1
Deduct 66 from 90 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 8:
66 goes into 240 3 times with a remainder of 42.
The next digit of our result is 3. 
Result so far: 3116.13
Deduct 198 from 240 and we're left with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Moving on to step 9:
The number 66 fits into 420 6 times, leaving a remainder of 24.
Put 6 as the next digit of the answer. 
Result so far: 3116.136
If we subtract 396 from 420, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 10:
66 goes into 240 3 times with a remainder of 42.
The number 3 becomes the next digit in our result. 
Result so far: 3116.1363
The remainder is 42 after subtracting 198 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 11:
66 goes into 420 6 times with a remainder of 24.
Put 6 as the next digit of the answer. 
Result so far: 3116.13636
Subtract 396 from 420 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 12:
66 can be fit into 240 3 times, resulting in a remainder of 42.
Put 3 as the next digit of the answer. 
Result so far: 3116.136363
If we take 198 away from 240, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 13:
66 can be fit into 420 6 times, resulting in a remainder of 24.
Write down 6 as next digit of the result. 
Result so far: 3116.1363636
If we subtract 396 from 420, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 14:
66 can be fit into 240 3 times, resulting in a remainder of 42.
Record the quotient 3 as the next digit in the result. 
Result so far: 3116.13636363
If we take 198 away from 240, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

The final outcome is 3116.13636363, with a leftover of 4.2e-08.