503519 ÷ 45 
We want to divide 503519 by 45.

Step 1:
5 divided by 45 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 45

Moving on to step 2:
When dividing 50 by 45, we get 1 with a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 45 from 50 and we're left with 5.
Fetch the next digit (3) from the dividend, attach it to 5 and continue: 53 / 45

Going ahead to step 3:
45 can be fit into 53 1 times, resulting in a remainder of 8.
Put 1 as the next digit of the answer. 
Result so far: 11.0
Subtract 45 from 53 to get 8.
Include the next digit (5) from the dividend after 8, then repeat: 85 / 45

On to step 4:
The number 45 fits into 85 1 times, leaving a remainder of 40.
The number 1 becomes the next digit in our result. 
Result so far: 111.0
If we subtract 45 from 85, we get 40.
Fetch the next digit (1) from the dividend, attach it to 40 and continue: 401 / 45

Let's proceed to step 5:
45 can be fit into 401 8 times, resulting in a remainder of 41.
Write down 8 as next digit of the result. 
Result so far: 1118.0
Subtracting 360 from 401 leaves us with 41.
Bring next digit (9) of the dividend behind the 41 and repeat the process: 419 / 45

Step 6:
When dividing 419 by 45, we get 9 with a remainder of 14.
Record the quotient 9 as the next digit in the result. 
Result so far: 11189.0
If we subtract 405 from 419, we get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 7:
The number 45 fits into 140 3 times, leaving a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 11189.3
Subtracting 135 from 140 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
When dividing 50 by 45, we get 1 with a remainder of 5.
The number 1 becomes the next digit in our result. 
Result so far: 11189.31
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 9:
45 can be fit into 50 1 times, resulting in a remainder of 5.
The next digit of our result is 1. 
Result so far: 11189.311
If we take 45 away from 50, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 11189.311, and the remainder is 0.0005.