344043 ÷ 66 
Let's see how many times 66 fits into 344043.

Going ahead to step 1:
When dividing 3 by 66, we get 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 66

Moving on to step 2:
If we divide 34 by 66, we get 0 and a remainder of 34.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 34 to get 34.
Include the next digit (4) from the dividend after 34, then repeat: 344 / 66

Let's proceed to step 3:
If we divide 344 by 66, we get 5 and a remainder of 14.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we subtract 330 from 344, we get 14.
Append the next digit (0) from the dividend to 14 and continue with: 140 / 66

Going ahead to step 4:
66 goes into 140 2 times with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 52.0
Subtract 132 from 140 to get 8.
Bring next digit (4) of the dividend behind the 8 and repeat the process: 84 / 66

Step 5:
If we divide 84 by 66, we get 1 and a remainder of 18.
Write down 1 as next digit of the result. 
Result so far: 521.0
Deduct 66 from 84 and we're left with 18.
Take the next digit (3) from the dividend and append it to 18, then repeat: 183 / 66

Going ahead to step 6:
183 divided by 66 is 2 with a remainder of 51.
Write down 2 as next digit of the result. 
Result so far: 5212.0
The remainder is 51 after subtracting 132 from 183.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Advancing to step 7:
66 can be fit into 510 7 times, resulting in a remainder of 48.
Record the quotient 7 as the next digit in the result. 
Result so far: 5212.7
Subtracting 462 from 510 leaves us with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

On to step 8:
66 goes into 480 7 times with a remainder of 18.
The next digit of our result is 7. 
Result so far: 5212.77
If we subtract 462 from 480, we 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.

The final outcome is 5212.77, with a leftover of 0.018.