We look at the division of 4329641 by 665 
Our goal is to divide 4329641 by 665.

On to step 1:
665 can be fit into 4 0 times, resulting in a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Fetch the next digit (3) from the dividend, attach it to 4 and continue: 43 / 665

Moving on to step 2:
665 can be fit into 43 0 times, resulting in a remainder of 43.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 43 to get 43.
Grab the next digit (2) from the dividend, add it to 43, then carry on: 432 / 665

Going ahead to step 3:
432 divided by 665 is 0 with a remainder of 432.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 432 and we're left with 432.
Fetch the next digit (9) from the dividend, attach it to 432 and continue: 4329 / 665

Step 4:
4329 divided by 665 is 6 with a remainder of 339.
The next digit of our result is 6. 
Result so far: 6.0
If we take 3990 away from 4329, we end up with 339.
Fetch the next digit (6) from the dividend, attach it to 339 and continue: 3396 / 665

Step 5:
665 can be fit into 3396 5 times, resulting in a remainder of 71.
The number 5 becomes the next digit in our result. 
Result so far: 65.0
If we take 3325 away from 3396, we end up with 71.
Take the next digit (4) from the dividend and append it to 71, then repeat: 714 / 665

Moving on to step 6:
665 goes into 714 1 times with a remainder of 49.
Put 1 as the next digit of the answer. 
Result so far: 651.0
Subtracting 665 from 714 leaves us with 49.
Append the next digit (1) from the dividend to 49 and continue with: 491 / 665

Advancing to step 7:
The number 665 fits into 491 0 times, leaving a remainder of 491.
The number 0 becomes the next digit in our result. 
Result so far: 6510.0
Deduct 0 from 491 and we're left with 491.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4910, and continue the process.

Let's proceed to step 8:
4910 divided by 665 is 7 with a remainder of 255.
Use 7 as the next digit of our solution. 
Result so far: 6510.7
The remainder is 255 after subtracting 4655 from 4910.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2550, and continue the process.

Step 9:
If we divide 2550 by 665, we get 3 and a remainder of 555.
Record the quotient 3 as the next digit in the result. 
Result so far: 6510.73
If we take 1995 away from 2550, we end up with 555.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5550, and continue the process.

Advancing to step 10:
If we divide 5550 by 665, we get 8 and a remainder of 230.
The next digit of our result is 8. 
Result so far: 6510.738
The remainder is 230 after subtracting 5320 from 5550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2300, and continue the process.

Advancing to step 11:
The number 665 fits into 2300 3 times, leaving a remainder of 305.
Write down 3 as next digit of the result. 
Result so far: 6510.7383
The remainder is 305 after subtracting 1995 from 2300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3050, and continue the process.

Going ahead to step 12:
If we divide 3050 by 665, we get 4 and a remainder of 390.
The number 4 becomes the next digit in our result. 
Result so far: 6510.73834
Subtract 2660 from 3050 to get 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3900, and continue the process.

Let's proceed to step 13:
The number 665 fits into 3900 5 times, leaving a remainder of 575.
Put 5 as the next digit of the answer. 
Result so far: 6510.738345
If we subtract 3325 from 3900, we get 575.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5750, and continue the process.

Moving on to step 14:
The number 665 fits into 5750 8 times, leaving a remainder of 430.
The next digit of our result is 8. 
Result so far: 6510.7383458
The remainder is 430 after subtracting 5320 from 5750.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4300, and continue the process.

Step 15:
665 goes into 4300 6 times with a remainder of 310.
The next digit of our result is 6. 
Result so far: 6510.73834586
Deduct 3990 from 4300 and we're left with 310.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3100, and continue the process.

The final result is 6510.73834586 with a remainder of 3.1e-07.