We look at the division of 450164 by 45 
Our goal is to divide 450164 by 45.

On to step 1:
If we divide 4 by 45, we get 0 and a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 45

On to step 2:
45 goes into 45 1 times with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 45 from 45, we get 0.
Append the next digit (0) from the dividend to 0 and continue with: 0 / 45

Moving on to step 3:
0 divided by 45 is 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 10.0
If we take 0 away from 0, we end up with 0.
Take the next digit (1) from the dividend and append it to 0, then repeat: 1 / 45

Advancing to step 4:
45 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 100.0
Subtract 0 from 1 to get 1.
Append the next digit (6) from the dividend to 1 and continue with: 16 / 45

Going ahead to step 5:
45 goes into 16 0 times with a remainder of 16.
Use 0 as the next digit of our solution. 
Result so far: 1000.0
Subtracting 0 from 16 leaves us with 16.
Take the next digit (4) from the dividend and append it to 16, then repeat: 164 / 45

Moving on to step 6:
The number 45 fits into 164 3 times, leaving a remainder of 29.
The number 3 becomes the next digit in our result. 
Result so far: 10003.0
Subtracting 135 from 164 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Going ahead to step 7:
The number 45 fits into 290 6 times, leaving a remainder of 20.
The next digit of our result is 6. 
Result so far: 10003.6
If we subtract 270 from 290, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 8:
If we divide 200 by 45, we get 4 and a remainder of 20.
The number 4 becomes the next digit in our result. 
Result so far: 10003.64
If we subtract 180 from 200, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 9:
45 goes into 200 4 times with a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 10003.644
Subtracting 180 from 200 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The quotient of the division is 10003.644, and the remainder is 0.002.