We look at the division of 34657 by 66 
Our goal is to divide 34657 by 66.

Going ahead to step 1:
The number 66 fits into 3 0 times, leaving a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (4) from the dividend and append it to 3, then repeat: 34 / 66

Advancing to step 2:
34 divided by 66 is 0 with a remainder of 34.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 34 and we're left with 34.
Take the next digit (6) from the dividend and append it to 34, then repeat: 346 / 66

Moving on to step 3:
66 can be fit into 346 5 times, resulting in a remainder of 16.
Write down 5 as next digit of the result. 
Result so far: 5.0
If we take 330 away from 346, we end up with 16.
Include the next digit (5) from the dividend after 16, then repeat: 165 / 66

Step 4:
The number 66 fits into 165 2 times, leaving a remainder of 33.
The next digit of our result is 2. 
Result so far: 52.0
Subtract 132 from 165 to get 33.
Bring next digit (7) of the dividend behind the 33 and repeat the process: 337 / 66

Going ahead to step 5:
The number 66 fits into 337 5 times, leaving a remainder of 7.
Use 5 as the next digit of our solution. 
Result so far: 525.0
Subtracting 330 from 337 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 6:
70 divided by 66 is 1 with a remainder of 4.
Use 1 as the next digit of our solution. 
Result so far: 525.1
The remainder is 4 after subtracting 66 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 7:
66 goes into 40 0 times with a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 525.1
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 8:
400 divided by 66 is 6 with a remainder of 4.
Put 6 as the next digit of the answer. 
Result so far: 525.106
Deduct 396 from 400 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 9:
40 divided by 66 is 0 with a remainder of 40.
The number 0 becomes the next digit in our result. 
Result so far: 525.106
The remainder is 40 after subtracting 0 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Let's proceed to step 10:
66 can be fit into 400 6 times, resulting in a remainder of 4.
Use 6 as the next digit of our solution. 
Result so far: 525.10606
If we take 396 away from 400, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 11:
66 goes into 40 0 times with a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 525.10606
If we subtract 0 from 40, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 12:
When dividing 400 by 66, we get 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 525.1060606
Deduct 396 from 400 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 13:
40 divided by 66 is 0 with a remainder of 40.
The next digit of our result is 0. 
Result so far: 525.1060606
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

The quotient of the division is 525.1060606, and the remainder is 4e-08.