We're dividing 566638 by 3 
We want to figure out the number of times 566638 can be divided by 3.

Moving on to step 1:
3 can be fit into 5 1 times, resulting in a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 3 from 5 to get 2.
Include the next digit (6) from the dividend after 2, then repeat: 26 / 3

Going ahead to step 2:
When dividing 26 by 3, we get 8 with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 18.0
If we subtract 24 from 26, we get 2.
Take the next digit (6) from the dividend and append it to 2, then repeat: 26 / 3

On to step 3:
3 can be fit into 26 8 times, resulting in a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 188.0
Deduct 24 from 26 and we're left with 2.
Include the next digit (6) from the dividend after 2, then repeat: 26 / 3

Step 4:
If we divide 26 by 3, we get 8 and a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 1888.0
The remainder is 2 after subtracting 24 from 26.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 3

Advancing to step 5:
When dividing 23 by 3, we get 7 with a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 18887.0
Deduct 21 from 23 and we're left with 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 3

Going ahead to step 6:
When dividing 28 by 3, we get 9 with a remainder of 1.
The next digit of our result is 9. 
Result so far: 188879.0
Subtracting 27 from 28 leaves us 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 7:
3 goes into 10 3 times with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 188879.3
If we subtract 9 from 10, we get 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 8:
10 divided by 3 is 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 188879.33
Deduct 9 from 10 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.

The final result is 188879.33 with a remainder of 0.001.