403109 ÷ 66 
We're looking to find how many times 66 goes into 403109.

Going ahead to step 1:
If we divide 4 by 66, we get 0 and a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Grab the next digit (0) from the dividend, add it to 4, then carry on: 40 / 66

Let's proceed to step 2:
The number 66 fits into 40 0 times, leaving a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 40, we get 40.
Append the next digit (3) from the dividend to 40 and continue with: 403 / 66

Advancing to step 3:
If we divide 403 by 66, we get 6 and a remainder of 7.
Put 6 as the next digit of the answer. 
Result so far: 6.0
Deduct 396 from 403 and we're left with 7.
Take the next digit (1) from the dividend and append it to 7, then repeat: 71 / 66

Moving on to step 4:
71 divided by 66 is 1 with a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 61.0
If we take 66 away from 71, we end up with 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 66

Step 5:
66 goes into 50 0 times with a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 610.0
The remainder is 50 after subtracting 0 from 50.
Include the next digit (9) from the dividend after 50, then repeat: 509 / 66

Moving on to step 6:
509 divided by 66 is 7 with a remainder of 47.
The number 7 becomes the next digit in our result. 
Result so far: 6107.0
Subtract 462 from 509 to get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Moving on to step 7:
66 can be fit into 470 7 times, resulting in a remainder of 8.
The number 7 becomes the next digit in our result. 
Result so far: 6107.7
Subtract 462 from 470 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 8:
80 divided by 66 is 1 with a remainder of 14.
The next digit of our result is 1. 
Result so far: 6107.71
Subtract 66 from 80 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 9:
The number 66 fits into 140 2 times, leaving a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 6107.712
Subtracting 132 from 140 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 10:
When dividing 80 by 66, we get 1 with a remainder of 14.
The number 1 becomes the next digit in our result. 
Result so far: 6107.7121
Deduct 66 from 80 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Step 11:
If we divide 140 by 66, we get 2 and a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 6107.71212
The remainder is 8 after subtracting 132 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 12:
66 goes into 80 1 times with a remainder of 14.
Record the quotient 1 as the next digit in the result. 
Result so far: 6107.712121
Deduct 66 from 80 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 13:
66 goes into 140 2 times with a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 6107.7121212
Subtract 132 from 140 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 14:
If we divide 80 by 66, we get 1 and a remainder of 14.
The next digit of our result is 1. 
Result so far: 6107.71212121
If we take 66 away from 80, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

The final result is 6107.71212121 with a remainder of 1.4e-08.