We look at the division of 414831 by 45 
We want to divide 414831 by 45.

Step 1:
When dividing 4 by 45, we get 0 with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Fetch the next digit (1) from the dividend, attach it to 4 and continue: 41 / 45

Advancing to step 2:
45 can be fit into 41 0 times, resulting in a remainder of 41.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 41, we get 41.
Append the next digit (4) from the dividend to 41 and continue with: 414 / 45

Let's proceed to step 3:
The number 45 fits into 414 9 times, leaving a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 9.0
Deduct 405 from 414 and we're left with 9.
Take the next digit (8) from the dividend and append it to 9, then repeat: 98 / 45

Step 4:
45 goes into 98 2 times with a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 92.0
Subtract 90 from 98 to get 8.
Take the next digit (3) from the dividend and append it to 8, then repeat: 83 / 45

On to step 5:
45 goes into 83 1 times with a remainder of 38.
Record the quotient 1 as the next digit in the result. 
Result so far: 921.0
If we subtract 45 from 83, we get 38.
Fetch the next digit (1) from the dividend, attach it to 38 and continue: 381 / 45

Let's proceed to step 6:
45 goes into 381 8 times with a remainder of 21.
Write down 8 as next digit of the result. 
Result so far: 9218.0
If we take 360 away from 381, we end up with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Going ahead to step 7:
45 goes into 210 4 times with a remainder of 30.
Write down 4 as next digit of the result. 
Result so far: 9218.4
Subtracting 180 from 210 leaves us 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.

Advancing to step 8:
If we divide 300 by 45, we get 6 and a remainder of 30.
The next digit of our result is 6. 
Result so far: 9218.46
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.

Moving on to step 9:
300 divided by 45 is 6 with a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 9218.466
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.

The quotient of the division is 9218.466, and the remainder is 0.003.