We look at the division of 378431 by 45 
We're looking to find how many times 45 goes into 378431.

Going ahead to step 1:
45 can be fit into 3 0 times, resulting in a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Include the next digit (7) from the dividend after 3, then repeat: 37 / 45

Advancing to step 2:
If we divide 37 by 45, we get 0 and a remainder of 37.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 37, we end up with 37.
Fetch the next digit (8) from the dividend, attach it to 37 and continue: 378 / 45

Going ahead to step 3:
When dividing 378 by 45, we get 8 with a remainder of 18.
The next digit of our result is 8. 
Result so far: 8.0
If we take 360 away from 378, we end up with 18.
Fetch the next digit (4) from the dividend, attach it to 18 and continue: 184 / 45

Let's proceed to step 4:
The number 45 fits into 184 4 times, leaving a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 84.0
If we take 180 away from 184, we end up with 4.
Append the next digit (3) from the dividend to 4 and continue with: 43 / 45

Going ahead to step 5:
When dividing 43 by 45, we get 0 with a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 840.0
Deduct 0 from 43 and we're left with 43.
Bring next digit (1) of the dividend behind the 43 and repeat the process: 431 / 45

Advancing to step 6:
45 goes into 431 9 times with a remainder of 26.
Use 9 as the next digit of our solution. 
Result so far: 8409.0
The remainder is 26 after subtracting 405 from 431.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

On to step 7:
The number 45 fits into 260 5 times, leaving a remainder of 35.
Write down 5 as next digit of the result. 
Result so far: 8409.5
The remainder is 35 after subtracting 225 from 260.
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 8:
45 can be fit into 350 7 times, resulting in a remainder of 35.
Write down 7 as next digit of the result. 
Result so far: 8409.57
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.

Going ahead to step 9:
45 goes into 350 7 times with a remainder of 35.
The number 7 becomes the next digit in our result. 
Result so far: 8409.577
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.

Our division results in 8409.577 with a remaining 0.0035.