14117 ÷ 66 
We're looking to find how many times 66 goes into 14117.

Advancing to step 1:
If we divide 1 by 66, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 66

On to step 2:
66 can be fit into 14 0 times, resulting in a remainder of 14.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 14 after subtracting 0 from 14.
Append the next digit (1) from the dividend to 14 and continue with: 141 / 66

Let's proceed to step 3:
When dividing 141 by 66, we get 2 with a remainder of 9.
Put 2 as the next digit of the answer. 
Result so far: 2.0
Subtract 132 from 141 to get 9.
Bring next digit (1) of the dividend behind the 9 and repeat the process: 91 / 66

On to step 4:
66 can be fit into 91 1 times, resulting in a remainder of 25.
The number 1 becomes the next digit in our result. 
Result so far: 21.0
Deduct 66 from 91 and we're left with 25.
Take the next digit (7) from the dividend and append it to 25, then repeat: 257 / 66

Moving on to step 5:
66 can be fit into 257 3 times, resulting in a remainder of 59.
Record the quotient 3 as the next digit in the result. 
Result so far: 213.0
If we take 198 away from 257, we end up with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Advancing to step 6:
The number 66 fits into 590 8 times, leaving a remainder of 62.
The next digit of our result is 8. 
Result so far: 213.8
Deduct 528 from 590 and we're left with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Moving on to step 7:
66 can be fit into 620 9 times, resulting in a remainder of 26.
Record the quotient 9 as the next digit in the result. 
Result so far: 213.89
If we subtract 594 from 620, we 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 8:
When dividing 260 by 66, we get 3 with a remainder of 62.
Put 3 as the next digit of the answer. 
Result so far: 213.893
If we subtract 198 from 260, we get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Let's proceed to step 9:
When dividing 620 by 66, we get 9 with a remainder of 26.
Put 9 as the next digit of the answer. 
Result so far: 213.8939
Deduct 594 from 620 and we're left with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 10:
The number 66 fits into 260 3 times, leaving a remainder of 62.
Use 3 as the next digit of our solution. 
Result so far: 213.89393
Subtract 198 from 260 to get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Let's proceed to step 11:
620 divided by 66 is 9 with a remainder of 26.
The number 9 becomes the next digit in our result. 
Result so far: 213.893939
Subtracting 594 from 620 leaves us with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 12:
66 goes into 260 3 times with a remainder of 62.
Record the quotient 3 as the next digit in the result. 
Result so far: 213.8939393
Subtracting 198 from 260 leaves us with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Moving on to step 13:
620 divided by 66 is 9 with a remainder of 26.
Write down 9 as next digit of the result. 
Result so far: 213.89393939
The remainder is 26 after subtracting 594 from 620.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

The final outcome is 213.89393939, with a leftover of 2.6e-08.