We look at the division of 905003 by 13 
Let's see how many times 13 fits into 905003.

Step 1:
If we divide 9 by 13, we get 0 and a remainder of 9.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 9 after subtracting 0 from 9.
Include the next digit (0) from the dividend after 9, then repeat: 90 / 13

Going ahead to step 2:
If we divide 90 by 13, we get 6 and a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 78 from 90, we get 12.
Fetch the next digit (5) from the dividend, attach it to 12 and continue: 125 / 13

On to step 3:
When dividing 125 by 13, we get 9 with a remainder of 8.
Use 9 as the next digit of our solution. 
Result so far: 69.0
Deduct 117 from 125 and we're left with 8.
Append the next digit (0) from the dividend to 8 and continue with: 80 / 13

Moving on to step 4:
The number 13 fits into 80 6 times, leaving a remainder of 2.
Use 6 as the next digit of our solution. 
Result so far: 696.0
The remainder is 2 after subtracting 78 from 80.
Fetch the next digit (0) from the dividend, attach it to 2 and continue: 20 / 13

Let's proceed to step 5:
When dividing 20 by 13, we get 1 with a remainder of 7.
The next digit of our result is 1. 
Result so far: 6961.0
Subtract 13 from 20 to get 7.
Grab the next digit (3) from the dividend, add it to 7, then carry on: 73 / 13

Step 6:
The number 13 fits into 73 5 times, leaving a remainder of 8.
Put 5 as the next digit of the answer. 
Result so far: 69615.0
Subtract 65 from 73 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 7:
If we divide 80 by 13, we get 6 and a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 69615.6
If we take 78 away from 80, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 8:
13 can be fit into 20 1 times, resulting in a remainder of 7.
The next digit of our result is 1. 
Result so far: 69615.61
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 9:
When dividing 70 by 13, we get 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 69615.615
If we take 65 away from 70, 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.

Advancing to step 10:
The number 13 fits into 50 3 times, leaving a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 69615.6153
If we take 39 away from 50, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 11:
13 goes into 110 8 times with a remainder of 6.
Record the quotient 8 as the next digit in the result. 
Result so far: 69615.61538
The remainder is 6 after subtracting 104 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 12:
13 can be fit into 60 4 times, resulting in a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 69615.615384
Subtracting 52 from 60 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Moving on to step 13:
The number 13 fits into 80 6 times, leaving a remainder of 2.
The next digit of our result is 6. 
Result so far: 69615.6153846
If we subtract 78 from 80, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 14:
The number 13 fits into 20 1 times, leaving a remainder of 7.
The next digit of our result is 1. 
Result so far: 69615.61538461
Subtracting 13 from 20 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

The quotient of the division is 69615.61538461, and the remainder is 7e-09.