We're dividing 386666 by 90 
We want to figure out the number of times 386666 can be divided by 90.

Step 1:
When dividing 3 by 90, we get 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Grab the next digit (8) from the dividend, add it to 3, then carry on: 38 / 90

Moving on to step 2:
The number 90 fits into 38 0 times, leaving a remainder of 38.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 38 and we're left with 38.
Take the next digit (6) from the dividend and append it to 38, then repeat: 386 / 90

Going ahead to step 3:
90 can be fit into 386 4 times, resulting in a remainder of 26.
Write down 4 as next digit of the result. 
Result so far: 4.0
Deduct 360 from 386 and we're left with 26.
Append the next digit (6) from the dividend to 26 and continue with: 266 / 90

Step 4:
The number 90 fits into 266 2 times, leaving a remainder of 86.
The number 2 becomes the next digit in our result. 
Result so far: 42.0
If we take 180 away from 266, we end up with 86.
Bring next digit (6) of the dividend behind the 86 and repeat the process: 866 / 90

On to step 5:
When dividing 866 by 90, we get 9 with a remainder of 56.
Use 9 as the next digit of our solution. 
Result so far: 429.0
Subtract 810 from 866 to get 56.
Append the next digit (6) from the dividend to 56 and continue with: 566 / 90

Going ahead to step 6:
If we divide 566 by 90, we get 6 and a remainder of 26.
The number 6 becomes the next digit in our result. 
Result so far: 4296.0
Subtract 540 from 566 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 7:
260 divided by 90 is 2 with a remainder of 80.
Use 2 as the next digit of our solution. 
Result so far: 4296.2
The remainder is 80 after subtracting 180 from 260.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Let's proceed to step 8:
800 divided by 90 is 8 with a remainder of 80.
Put 8 as the next digit of the answer. 
Result so far: 4296.28
Deduct 720 from 800 and we're left with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Let's proceed to step 9:
When dividing 800 by 90, we get 8 with a remainder of 80.
Record the quotient 8 as the next digit in the result. 
Result so far: 4296.288
The remainder is 80 after subtracting 720 from 800.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

The quotient of the division is 4296.288, and the remainder is 0.008.