We look at the division of 37635 by 66 
Let's see how many times 66 fits into 37635.

Moving on to step 1:
66 can be fit into 3 0 times, resulting in a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 66

Let's proceed to step 2:
The number 66 fits into 37 0 times, leaving a remainder of 37.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 37, we get 37.
Grab the next digit (6) from the dividend, add it to 37, then carry on: 376 / 66

Moving on to step 3:
66 goes into 376 5 times with a remainder of 46.
The next digit of our result is 5. 
Result so far: 5.0
The remainder is 46 after subtracting 330 from 376.
Fetch the next digit (3) from the dividend, attach it to 46 and continue: 463 / 66

Advancing to step 4:
463 divided by 66 is 7 with a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 57.0
Subtracting 462 from 463 leaves us with 1.
Include the next digit (5) from the dividend after 1, then repeat: 15 / 66

Let's proceed to step 5:
The number 66 fits into 15 0 times, leaving a remainder of 15.
The next digit of our result is 0. 
Result so far: 570.0
Deduct 0 from 15 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 6:
66 can be fit into 150 2 times, resulting in a remainder of 18.
Use 2 as the next digit of our solution. 
Result so far: 570.2
Subtract 132 from 150 to 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.

Let's proceed to step 7:
If we divide 180 by 66, we get 2 and a remainder of 48.
Record the quotient 2 as the next digit in the result. 
Result so far: 570.22
The remainder is 48 after subtracting 132 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

The final outcome is 570.22, with a leftover of 0.048.