501261 ÷ 66 
Our goal is to divide 501261 by 66.

Moving on to step 1:
66 goes into 5 0 times with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 66

On to step 2:
50 divided by 66 is 0 with a remainder of 50.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 50 and we're left with 50.
Bring next digit (1) of the dividend behind the 50 and repeat the process: 501 / 66

Moving on to step 3:
501 divided by 66 is 7 with a remainder of 39.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Deduct 462 from 501 and we're left with 39.
Fetch the next digit (2) from the dividend, attach it to 39 and continue: 392 / 66

Let's proceed to step 4:
392 divided by 66 is 5 with a remainder of 62.
Use 5 as the next digit of our solution. 
Result so far: 75.0
If we take 330 away from 392, we end up with 62.
Fetch the next digit (6) from the dividend, attach it to 62 and continue: 626 / 66

Going ahead to step 5:
If we divide 626 by 66, we get 9 and a remainder of 32.
Record the quotient 9 as the next digit in the result. 
Result so far: 759.0
If we subtract 594 from 626, we get 32.
Include the next digit (1) from the dividend after 32, then repeat: 321 / 66

Step 6:
The number 66 fits into 321 4 times, leaving a remainder of 57.
Use 4 as the next digit of our solution. 
Result so far: 7594.0
The remainder is 57 after subtracting 264 from 321.
Since there are no more digits in the dividend, we add a zero to the remainder making it 570, and continue the process.

Going ahead to step 7:
66 goes into 570 8 times with a remainder of 42.
Use 8 as the next digit of our solution. 
Result so far: 7594.8
Deduct 528 from 570 and we're left with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 8:
420 divided by 66 is 6 with a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 7594.86
The remainder is 24 after subtracting 396 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Going ahead to step 9:
66 goes into 240 3 times with a remainder of 42.
Use 3 as the next digit of our solution. 
Result so far: 7594.863
Subtracting 198 from 240 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Moving on to step 10:
When dividing 420 by 66, we get 6 with a remainder of 24.
Record the quotient 6 as the next digit in the result. 
Result so far: 7594.8636
If we subtract 396 from 420, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 11:
If we divide 240 by 66, we get 3 and a remainder of 42.
Record the quotient 3 as the next digit in the result. 
Result so far: 7594.86363
If we subtract 198 from 240, we get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Going ahead to step 12:
420 divided by 66 is 6 with a remainder of 24.
The next digit of our result is 6. 
Result so far: 7594.863636
The remainder is 24 after subtracting 396 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 13:
The number 66 fits into 240 3 times, leaving a remainder of 42.
Use 3 as the next digit of our solution. 
Result so far: 7594.8636363
Subtracting 198 from 240 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 14:
66 goes into 420 6 times with a remainder of 24.
Write down 6 as next digit of the result. 
Result so far: 7594.86363636
Subtract 396 from 420 to get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

The final result is 7594.86363636 with a remainder of 2.4e-08.