We're dividing 437797 by 45 
We're looking to find how many times 45 goes into 437797.

On to step 1:
When dividing 4 by 45, we get 0 with a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 45

Let's proceed to step 2:
43 divided by 45 is 0 with a remainder of 43.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 43 to get 43.
Include the next digit (7) from the dividend after 43, then repeat: 437 / 45

Moving on to step 3:
If we divide 437 by 45, we get 9 and a remainder of 32.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
The remainder is 32 after subtracting 405 from 437.
Fetch the next digit (7) from the dividend, attach it to 32 and continue: 327 / 45

On to step 4:
If we divide 327 by 45, we get 7 and a remainder of 12.
Put 7 as the next digit of the answer. 
Result so far: 97.0
If we subtract 315 from 327, we get 12.
Take the next digit (9) from the dividend and append it to 12, then repeat: 129 / 45

On to step 5:
45 goes into 129 2 times with a remainder of 39.
The next digit of our result is 2. 
Result so far: 972.0
Subtract 90 from 129 to get 39.
Include the next digit (7) from the dividend after 39, then repeat: 397 / 45

Let's proceed to step 6:
If we divide 397 by 45, we get 8 and a remainder of 37.
The next digit of our result is 8. 
Result so far: 9728.0
Subtract 360 from 397 to get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

Step 7:
370 divided by 45 is 8 with a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 9728.8
If we subtract 360 from 370, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 8:
If we divide 100 by 45, we get 2 and a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 9728.82
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 9:
45 can be fit into 100 2 times, resulting in a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 9728.822
Deduct 90 from 100 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 9728.822, and the remainder is 0.001.