10105 ÷ 66 
Our goal is to divide 10105 by 66.

Step 1:
1 divided by 66 is 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 66

On to step 2:
10 divided by 66 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Append the next digit (1) from the dividend to 10 and continue with: 101 / 66

Step 3:
The number 66 fits into 101 1 times, leaving a remainder of 35.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 66 from 101 to get 35.
Bring next digit (0) of the dividend behind the 35 and repeat the process: 350 / 66

On to step 4:
If we divide 350 by 66, we get 5 and a remainder of 20.
Write down 5 as next digit of the result. 
Result so far: 15.0
Deduct 330 from 350 and we're left with 20.
Grab the next digit (5) from the dividend, add it to 20, then carry on: 205 / 66

Step 5:
66 can be fit into 205 3 times, resulting in a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 153.0
Subtracting 198 from 205 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.

Going ahead to step 6:
66 can be fit into 70 1 times, resulting in a remainder of 4.
Use 1 as the next digit of our solution. 
Result so far: 153.1
If we take 66 away from 70, 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.

Step 7:
If we divide 40 by 66, we get 0 and a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 153.1
If we take 0 away from 40, we end up 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.

On to step 8:
If we divide 400 by 66, we get 6 and a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 153.106
Subtracting 396 from 400 leaves us 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.

Going ahead to step 9:
66 goes into 40 0 times with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 153.106
Subtracting 0 from 40 leaves us 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.

Advancing to step 10:
The number 66 fits into 400 6 times, leaving a remainder of 4.
The next digit of our result is 6. 
Result so far: 153.10606
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:
The number 66 fits into 40 0 times, leaving a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 153.10606
If we take 0 away from 40, we end up 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.

Moving on to step 12:
400 divided by 66 is 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 153.1060606
The remainder is 4 after subtracting 396 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 13:
40 divided by 66 is 0 with a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 153.1060606
Subtracting 0 from 40 leaves us 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.

The quotient of the division is 153.1060606, and the remainder is 4e-08.