We're dividing 39666 by 434 
We're looking to find how many times 434 goes into 39666.

Advancing to step 1:
434 goes into 3 0 times with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Append the next digit (9) from the dividend to 3 and continue with: 39 / 434

Going ahead to step 2:
434 goes into 39 0 times with a remainder of 39.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 39 and we're left with 39.
Append the next digit (6) from the dividend to 39 and continue with: 396 / 434

Advancing to step 3:
396 divided by 434 is 0 with a remainder of 396.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 396 leaves us with 396.
Take the next digit (6) from the dividend and append it to 396, then repeat: 3966 / 434

Moving on to step 4:
If we divide 3966 by 434, we get 9 and a remainder of 60.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
The remainder is 60 after subtracting 3906 from 3966.
Include the next digit (6) from the dividend after 60, then repeat: 606 / 434

Advancing to step 5:
434 can be fit into 606 1 times, resulting in a remainder of 172.
The number 1 becomes the next digit in our result. 
Result so far: 91.0
If we take 434 away from 606, we end up with 172.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1720, and continue the process.

Advancing to step 6:
434 can be fit into 1720 3 times, resulting in a remainder of 418.
Write down 3 as next digit of the result. 
Result so far: 91.3
The remainder is 418 after subtracting 1302 from 1720.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4180, and continue the process.

Step 7:
4180 divided by 434 is 9 with a remainder of 274.
Put 9 as the next digit of the answer. 
Result so far: 91.39
If we take 3906 away from 4180, we end up with 274.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2740, and continue the process.

Let's proceed to step 8:
The number 434 fits into 2740 6 times, leaving a remainder of 136.
Record the quotient 6 as the next digit in the result. 
Result so far: 91.396
The remainder is 136 after subtracting 2604 from 2740.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1360, and continue the process.

Going ahead to step 9:
1360 divided by 434 is 3 with a remainder of 58.
Record the quotient 3 as the next digit in the result. 
Result so far: 91.3963
If we subtract 1302 from 1360, we get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Let's proceed to step 10:
When dividing 580 by 434, we get 1 with a remainder of 146.
Write down 1 as next digit of the result. 
Result so far: 91.39631
If we subtract 434 from 580, we get 146.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1460, and continue the process.

Step 11:
If we divide 1460 by 434, we get 3 and a remainder of 158.
Use 3 as the next digit of our solution. 
Result so far: 91.396313
Deduct 1302 from 1460 and we're left with 158.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1580, and continue the process.

Let's proceed to step 12:
1580 divided by 434 is 3 with a remainder of 278.
The number 3 becomes the next digit in our result. 
Result so far: 91.3963133
Subtract 1302 from 1580 to get 278.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2780, and continue the process.

After the division, we end up with 91.3963133 and a remainder of 2.78e-06.