We divide 113314 by 3
We're looking to find how many times 3 goes into 113314.

Going ahead to step 1:
3 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 3

On to step 2:
11 divided by 3 is 3 with a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 3.0
If we take 9 away from 11, we end up with 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 3

Advancing to step 3:
3 can be fit into 23 7 times, resulting in a remainder of 2.
Use 7 as the next digit of our solution. 
Result so far: 37.0
The remainder is 2 after subtracting 21 from 23.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 3

Step 4:
When dividing 23 by 3, we get 7 with a remainder of 2.
The next digit of our result is 7. 
Result so far: 377.0
If we subtract 21 from 23, we get 2.
Take the next digit (1) from the dividend and append it to 2, then repeat: 21 / 3

Moving on to step 5:
21 divided by 3 is 7 with a remainder of 0.
The next digit of our result is 7. 
Result so far: 3777.0
If we subtract 21 from 21, we get 0.
Take the next digit (4) from the dividend and append it to 0, then repeat: 4 / 3

Moving on to step 6:
3 can be fit into 4 1 times, resulting in a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 37771.0
If we subtract 3 from 4, 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.

Let's proceed to step 7:
When dividing 10 by 3, we get 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 37771.3
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.

Step 8:
If we divide 10 by 3, we get 3 and a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 37771.33
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 outcome is 37771.33, with a leftover of 0.001.