We divide 37566 by 4
We want to figure out the number of times 37566 can be divided by 4.

Advancing to step 1:
4 can be fit into 3 0 times, resulting in a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 4

Moving on to step 2:
4 can be fit into 37 9 times, resulting in a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
The remainder is 1 after subtracting 36 from 37.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 4

Step 3:
4 goes into 15 3 times with a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 93.0
If we take 12 away from 15, we end up with 3.
Take the next digit (6) from the dividend and append it to 3, then repeat: 36 / 4

Step 4:
4 goes into 36 9 times with a remainder of 0.
The number 9 becomes the next digit in our result. 
Result so far: 939.0
The remainder is 0 after subtracting 36 from 36.
Grab the next digit (6) from the dividend, add it to 0, then carry on: 6 / 4

Let's proceed to step 5:
When dividing 6 by 4, we get 1 with a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 9391.0
Subtract 4 from 6 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 6:
20 divided by 4 is 5 with a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 9391.5
Subtracting 20 from 20 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 7:
If we divide 0 by 4, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 9391.5
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 8:
0 divided by 4 is 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 9391.5
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Our division results in 9391.5 with a remaining 0.0.