113666 divided by 3 
We're looking to find how many times 3 goes into 113666.

On to step 1:
The number 3 fits into 1 0 times, leaving 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.
Take the next digit (1) from the dividend and append it to 1, then repeat: 11 / 3

Going ahead to step 2:
3 can be fit into 11 3 times, resulting in a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
The remainder is 2 after subtracting 9 from 11.
Grab the next digit (3) from the dividend, add it to 2, then carry on: 23 / 3

Advancing to step 3:
The number 3 fits into 23 7 times, leaving a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 37.0
Deduct 21 from 23 and we're left with 2.
Take the next digit (6) from the dividend and append it to 2, then repeat: 26 / 3

On to step 4:
If we divide 26 by 3, we get 8 and a remainder of 2.
The next digit of our result is 8. 
Result so far: 378.0
Deduct 24 from 26 and we're left with 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 3

Moving on to step 5:
26 divided by 3 is 8 with a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 3788.0
If we take 24 away from 26, we end up with 2.
Take the next digit (6) from the dividend and append it to 2, then repeat: 26 / 3

Let's proceed to step 6:
The number 3 fits into 26 8 times, leaving a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 37888.0
If we subtract 24 from 26, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 7:
The number 3 fits into 20 6 times, leaving a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 37888.6
The remainder is 2 after subtracting 18 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
The number 3 fits into 20 6 times, leaving a remainder of 2.
Put 6 as the next digit of the answer. 
Result so far: 37888.66
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

The final result is 37888.66 with a remainder of 0.002.