37565 ÷ 45 
Our goal is to divide 37565 by 45.

Going ahead to step 1:
When dividing 3 by 45, we get 0 with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 45

Let's proceed to step 2:
45 can be fit into 37 0 times, resulting in a remainder of 37.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 37 leaves us with 37.
Take the next digit (5) from the dividend and append it to 37, then repeat: 375 / 45

Step 3:
375 divided by 45 is 8 with a remainder of 15.
The next digit of our result is 8. 
Result so far: 8.0
Subtract 360 from 375 to get 15.
Bring next digit (6) of the dividend behind the 15 and repeat the process: 156 / 45

Moving on to step 4:
45 goes into 156 3 times with a remainder of 21.
Put 3 as the next digit of the answer. 
Result so far: 83.0
If we subtract 135 from 156, we get 21.
Grab the next digit (5) from the dividend, add it to 21, then carry on: 215 / 45

Let's proceed to step 5:
When dividing 215 by 45, we get 4 with a remainder of 35.
Use 4 as the next digit of our solution. 
Result so far: 834.0
Subtracting 180 from 215 leaves us with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 6:
45 can be fit into 350 7 times, resulting in a remainder of 35.
The next digit of our result is 7. 
Result so far: 834.7
The remainder is 35 after subtracting 315 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Advancing to step 7:
If we divide 350 by 45, we get 7 and a remainder of 35.
Write down 7 as next digit of the result. 
Result so far: 834.77
If we subtract 315 from 350, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

The quotient of the division is 834.77, and the remainder is 0.035.