We're dividing 475603 by 45 
We want to figure out the number of times 475603 can be divided by 45.

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 take 0 away from 4, we end up with 4.
Grab the next digit (7) from the dividend, add it to 4, then carry on: 47 / 45

On to step 2:
47 divided by 45 is 1 with a remainder of 2.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtracting 45 from 47 leaves us with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 45

On to step 3:
25 divided by 45 is 0 with a remainder of 25.
Write down 0 as next digit of the result. 
Result so far: 10.0
The remainder is 25 after subtracting 0 from 25.
Include the next digit (6) from the dividend after 25, then repeat: 256 / 45

Step 4:
If we divide 256 by 45, we get 5 and a remainder of 31.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
If we subtract 225 from 256, we get 31.
Bring next digit (0) of the dividend behind the 31 and repeat the process: 310 / 45

On to step 5:
When dividing 310 by 45, we get 6 with a remainder of 40.
The next digit of our result is 6. 
Result so far: 1056.0
Deduct 270 from 310 and we're left with 40.
Take the next digit (3) from the dividend and append it to 40, then repeat: 403 / 45

On to step 6:
If we divide 403 by 45, we get 8 and a remainder of 43.
Put 8 as the next digit of the answer. 
Result so far: 10568.0
If we take 360 away from 403, we end up with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Let's proceed to step 7:
45 goes into 430 9 times with a remainder of 25.
Put 9 as the next digit of the answer. 
Result so far: 10568.9
If we take 405 away from 430, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
The number 45 fits into 250 5 times, leaving a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 10568.95
If we subtract 225 from 250, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 9:
The number 45 fits into 250 5 times, leaving a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 10568.955
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

After the division, we end up with 10568.955 and a remainder of 0.0025.