We're dividing 344905 by 66 
We're looking to find how many times 66 goes into 344905.

Going ahead to step 1:
66 can be fit into 3 0 times, resulting in a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Append the next digit (4) from the dividend to 3 and continue with: 34 / 66

On to step 2:
When dividing 34 by 66, we get 0 with a remainder of 34.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 34 after subtracting 0 from 34.
Bring next digit (4) of the dividend behind the 34 and repeat the process: 344 / 66

Advancing to step 3:
344 divided by 66 is 5 with a remainder of 14.
The next digit of our result is 5. 
Result so far: 5.0
If we take 330 away from 344, we end up with 14.
Include the next digit (9) from the dividend after 14, then repeat: 149 / 66

Step 4:
66 goes into 149 2 times with a remainder of 17.
The next digit of our result is 2. 
Result so far: 52.0
Deduct 132 from 149 and we're left with 17.
Grab the next digit (0) from the dividend, add it to 17, then carry on: 170 / 66

On to step 5:
66 can be fit into 170 2 times, resulting in a remainder of 38.
The number 2 becomes the next digit in our result. 
Result so far: 522.0
Subtract 132 from 170 to get 38.
Grab the next digit (5) from the dividend, add it to 38, then carry on: 385 / 66

Going ahead to step 6:
If we divide 385 by 66, we get 5 and a remainder of 55.
Put 5 as the next digit of the answer. 
Result so far: 5225.0
The remainder is 55 after subtracting 330 from 385.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 7:
550 divided by 66 is 8 with a remainder of 22.
Use 8 as the next digit of our solution. 
Result so far: 5225.8
Deduct 528 from 550 and we're left with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Advancing to step 8:
220 divided by 66 is 3 with a remainder of 22.
Use 3 as the next digit of our solution. 
Result so far: 5225.83
If we take 198 away from 220, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 9:
If we divide 220 by 66, we get 3 and a remainder of 22.
Record the quotient 3 as the next digit in the result. 
Result so far: 5225.833
Subtracting 198 from 220 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

After the division, we end up with 5225.833 and a remainder of 0.0022.