738617 ÷ 66 
Our goal is to divide 738617 by 66.

Let's proceed to step 1:
When dividing 7 by 66, we get 0 with a remainder of 7.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 7, we end up with 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 66

Step 2:
66 goes into 73 1 times with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Subtracting 66 from 73 leaves us with 7.
Append the next digit (8) from the dividend to 7 and continue with: 78 / 66

Going ahead to step 3:
66 goes into 78 1 times with a remainder of 12.
Put 1 as the next digit of the answer. 
Result so far: 11.0
Subtracting 66 from 78 leaves us with 12.
Bring next digit (6) of the dividend behind the 12 and repeat the process: 126 / 66

Going ahead to step 4:
The number 66 fits into 126 1 times, leaving a remainder of 60.
The number 1 becomes the next digit in our result. 
Result so far: 111.0
If we subtract 66 from 126, we get 60.
Bring next digit (1) of the dividend behind the 60 and repeat the process: 601 / 66

On to step 5:
If we divide 601 by 66, we get 9 and a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 1119.0
Subtract 594 from 601 to get 7.
Take the next digit (7) from the dividend and append it to 7, then repeat: 77 / 66

On to step 6:
When dividing 77 by 66, we get 1 with a remainder of 11.
Write down 1 as next digit of the result. 
Result so far: 11191.0
Subtract 66 from 77 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

On to step 7:
66 goes into 110 1 times with a remainder of 44.
Write down 1 as next digit of the result. 
Result so far: 11191.1
Subtract 66 from 110 to get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Moving on to step 8:
66 can be fit into 440 6 times, resulting in a remainder of 44.
Record the quotient 6 as the next digit in the result. 
Result so far: 11191.16
The remainder is 44 after subtracting 396 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Step 9:
If we divide 440 by 66, we get 6 and a remainder of 44.
Put 6 as the next digit of the answer. 
Result so far: 11191.166
The remainder is 44 after subtracting 396 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

In conclusion, the division gives 11191.166 with a balance of 0.0044.