We look at the division of 135003 by 3 
We're looking to find how many times 3 goes into 135003.

On to step 1:
If we divide 1 by 3, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 3

Let's proceed to step 2:
13 divided by 3 is 4 with a remainder of 1.
Write down 4 as next digit of the result. 
Result so far: 4.0
The remainder is 1 after subtracting 12 from 13.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 3

On to step 3:
3 can be fit into 15 5 times, resulting in a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 45.0
Deduct 15 from 15 and we're left with 0.
Append the next digit (0) from the dividend to 0 and continue with: 0 / 3

Step 4:
0 divided by 3 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 450.0
If we subtract 0 from 0, we get 0.
Grab the next digit (0) from the dividend, add it to 0, then carry on: 0 / 3

Moving on to step 5:
0 divided by 3 is 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 4500.0
If we subtract 0 from 0, we get 0.
Append the next digit (3) from the dividend to 0 and continue with: 3 / 3

Step 6:
3 goes into 3 1 times with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 45001.0
The remainder is 0 after subtracting 3 from 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 7:
When dividing 0 by 3, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 45001.0
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 8:
The number 3 fits into 0 0 times, leaving a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 45001.0
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The quotient of the division is 45001.0, and the remainder is 0.0.