603566 divided by 45 
Our goal is to divide 603566 by 45.

Going ahead to step 1:
The number 45 fits into 6 0 times, leaving a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Take the next digit (0) from the dividend and append it to 6, then repeat: 60 / 45

Advancing to step 2:
45 goes into 60 1 times with a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 15 after subtracting 45 from 60.
Fetch the next digit (3) from the dividend, attach it to 15 and continue: 153 / 45

Let's proceed to step 3:
45 goes into 153 3 times with a remainder of 18.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Deduct 135 from 153 and we're left with 18.
Fetch the next digit (5) from the dividend, attach it to 18 and continue: 185 / 45

Advancing to step 4:
45 goes into 185 4 times with a remainder of 5.
Put 4 as the next digit of the answer. 
Result so far: 134.0
Deduct 180 from 185 and we're left with 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 45

On to step 5:
When dividing 56 by 45, we get 1 with a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 1341.0
The remainder is 11 after subtracting 45 from 56.
Take the next digit (6) from the dividend and append it to 11, then repeat: 116 / 45

Going ahead to step 6:
45 can be fit into 116 2 times, resulting in a remainder of 26.
Put 2 as the next digit of the answer. 
Result so far: 13412.0
If we subtract 90 from 116, we get 26.
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:
If we divide 260 by 45, we get 5 and a remainder of 35.
Record the quotient 5 as the next digit in the result. 
Result so far: 13412.5
If we subtract 225 from 260, 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.

On to step 8:
45 can be fit into 350 7 times, resulting in a remainder of 35.
Use 7 as the next digit of our solution. 
Result so far: 13412.57
Subtract 315 from 350 to 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.

Moving on 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: 13412.577
If we take 315 away from 350, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

The quotient of the division is 13412.577, and the remainder is 0.0035.