33117 ÷ 66 
We're looking to find how many times 66 goes into 33117.

Advancing to step 1:
When dividing 3 by 66, 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 (3) from the dividend, add it to 3, then carry on: 33 / 66

Let's proceed to step 2:
When dividing 33 by 66, we get 0 with a remainder of 33.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 33 to get 33.
Take the next digit (1) from the dividend and append it to 33, then repeat: 331 / 66

On to step 3:
66 can be fit into 331 5 times, resulting in a remainder of 1.
The next digit of our result is 5. 
Result so far: 5.0
Subtracting 330 from 331 leaves us with 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 66

Let's proceed to step 4:
When dividing 11 by 66, we get 0 with a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 50.0
If we subtract 0 from 11, we get 11.
Grab the next digit (7) from the dividend, add it to 11, then carry on: 117 / 66

Going ahead to step 5:
66 can be fit into 117 1 times, resulting in a remainder of 51.
The number 1 becomes the next digit in our result. 
Result so far: 501.0
Subtracting 66 from 117 leaves us with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Step 6:
When dividing 510 by 66, we get 7 with a remainder of 48.
Put 7 as the next digit of the answer. 
Result so far: 501.7
The remainder is 48 after subtracting 462 from 510.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Step 7:
480 divided by 66 is 7 with a remainder of 18.
Record the quotient 7 as the next digit in the result. 
Result so far: 501.77
Subtract 462 from 480 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

The final outcome is 501.77, with a leftover of 0.018.