We're dividing 434691 by 66 
Let's see how many times 66 fits into 434691.

Let's proceed to step 1:
The number 66 fits into 4 0 times, leaving a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Include the next digit (3) from the dividend after 4, then repeat: 43 / 66

Let's proceed to step 2:
The number 66 fits into 43 0 times, leaving a remainder of 43.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 43 after subtracting 0 from 43.
Fetch the next digit (4) from the dividend, attach it to 43 and continue: 434 / 66

Going ahead to step 3:
If we divide 434 by 66, we get 6 and a remainder of 38.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
The remainder is 38 after subtracting 396 from 434.
Append the next digit (6) from the dividend to 38 and continue with: 386 / 66

Advancing to step 4:
66 goes into 386 5 times with a remainder of 56.
Put 5 as the next digit of the answer. 
Result so far: 65.0
Subtracting 330 from 386 leaves us with 56.
Grab the next digit (9) from the dividend, add it to 56, then carry on: 569 / 66

On to step 5:
If we divide 569 by 66, we get 8 and a remainder of 41.
Put 8 as the next digit of the answer. 
Result so far: 658.0
Subtracting 528 from 569 leaves us with 41.
Fetch the next digit (1) from the dividend, attach it to 41 and continue: 411 / 66

Step 6:
When dividing 411 by 66, we get 6 with a remainder of 15.
The next digit of our result is 6. 
Result so far: 6586.0
Deduct 396 from 411 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 7:
The number 66 fits into 150 2 times, leaving a remainder of 18.
Record the quotient 2 as the next digit in the result. 
Result so far: 6586.2
Subtract 132 from 150 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.

Moving on to step 8:
When dividing 180 by 66, we get 2 with a remainder of 48.
The number 2 becomes the next digit in our result. 
Result so far: 6586.22
Subtract 132 from 180 to get 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

The final outcome is 6586.22, with a leftover of 0.048.