We're dividing 436945 by 66 
Our goal is to divide 436945 by 66.

Let's proceed to step 1:
66 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 66

Moving on to step 2:
When dividing 43 by 66, we get 0 with a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 43, we end up with 43.
Append the next digit (6) from the dividend to 43 and continue with: 436 / 66

Moving on to step 3:
When dividing 436 by 66, we get 6 with a remainder of 40.
Put 6 as the next digit of the answer. 
Result so far: 6.0
If we take 396 away from 436, we end up with 40.
Grab the next digit (9) from the dividend, add it to 40, then carry on: 409 / 66

Step 4:
The number 66 fits into 409 6 times, leaving a remainder of 13.
Write down 6 as next digit of the result. 
Result so far: 66.0
Deduct 396 from 409 and we're left with 13.
Append the next digit (4) from the dividend to 13 and continue with: 134 / 66

Step 5:
When dividing 134 by 66, we get 2 with a remainder of 2.
Use 2 as the next digit of our solution. 
Result so far: 662.0
If we subtract 132 from 134, we get 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 66

On to step 6:
66 can be fit into 25 0 times, resulting in a remainder of 25.
Write down 0 as next digit of the result. 
Result so far: 6620.0
Deduct 0 from 25 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 7:
If we divide 250 by 66, we get 3 and a remainder of 52.
The number 3 becomes the next digit in our result. 
Result so far: 6620.3
Subtracting 198 from 250 leaves us with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Step 8:
520 divided by 66 is 7 with a remainder of 58.
Record the quotient 7 as the next digit in the result. 
Result so far: 6620.37
Deduct 462 from 520 and we're left with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Moving on to step 9:
When dividing 580 by 66, we get 8 with a remainder of 52.
Put 8 as the next digit of the answer. 
Result so far: 6620.378
If we subtract 528 from 580, we get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

On to step 10:
When dividing 520 by 66, we get 7 with a remainder of 58.
Put 7 as the next digit of the answer. 
Result so far: 6620.3787
Subtracting 462 from 520 leaves us with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Step 11:
66 can be fit into 580 8 times, resulting in a remainder of 52.
Put 8 as the next digit of the answer. 
Result so far: 6620.37878
If we subtract 528 from 580, we get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Step 12:
The number 66 fits into 520 7 times, leaving a remainder of 58.
Use 7 as the next digit of our solution. 
Result so far: 6620.378787
Deduct 462 from 520 and we're left with 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 13:
The number 66 fits into 580 8 times, leaving a remainder of 52.
The next digit of our result is 8. 
Result so far: 6620.3787878
The remainder is 52 after subtracting 528 from 580.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

On to step 14:
When dividing 520 by 66, we get 7 with a remainder of 58.
Use 7 as the next digit of our solution. 
Result so far: 6620.37878787
The remainder is 58 after subtracting 462 from 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

The final outcome is 6620.37878787, with a leftover of 5.8e-08.