37965 ÷ 45 
Let's see how many times 45 fits into 37965.

On to step 1:
The number 45 fits into 3 0 times, leaving a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 45

On to step 2:
If we divide 37 by 45, we get 0 and a remainder of 37.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 37 after subtracting 0 from 37.
Take the next digit (9) from the dividend and append it to 37, then repeat: 379 / 45

Advancing to step 3:
The number 45 fits into 379 8 times, leaving a remainder of 19.
Put 8 as the next digit of the answer. 
Result so far: 8.0
If we subtract 360 from 379, we get 19.
Include the next digit (6) from the dividend after 19, then repeat: 196 / 45

Advancing to step 4:
45 goes into 196 4 times with a remainder of 16.
The next digit of our result is 4. 
Result so far: 84.0
The remainder is 16 after subtracting 180 from 196.
Append the next digit (5) from the dividend to 16 and continue with: 165 / 45

Going ahead to step 5:
45 can be fit into 165 3 times, resulting in a remainder of 30.
Use 3 as the next digit of our solution. 
Result so far: 843.0
Subtract 135 from 165 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 6:
When dividing 300 by 45, we get 6 with a remainder of 30.
Use 6 as the next digit of our solution. 
Result so far: 843.6
Deduct 270 from 300 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 7:
The number 45 fits into 300 6 times, leaving a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 843.66
If we take 270 away from 300, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Our division results in 843.66 with a remaining 0.03.