We look at the division of 503281 by 65 
Our goal is to divide 503281 by 65.

Going ahead to step 1:
If we divide 5 by 65, we get 0 and a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 65

On to step 2:
If we divide 50 by 65, we get 0 and a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 50 to get 50.
Bring next digit (3) of the dividend behind the 50 and repeat the process: 503 / 65

Going ahead to step 3:
If we divide 503 by 65, we get 7 and a remainder of 48.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Subtracting 455 from 503 leaves us with 48.
Append the next digit (2) from the dividend to 48 and continue with: 482 / 65

Let's proceed to step 4:
If we divide 482 by 65, we get 7 and a remainder of 27.
Put 7 as the next digit of the answer. 
Result so far: 77.0
Deduct 455 from 482 and we're left with 27.
Append the next digit (8) from the dividend to 27 and continue with: 278 / 65

Going ahead to step 5:
The number 65 fits into 278 4 times, leaving a remainder of 18.
The next digit of our result is 4. 
Result so far: 774.0
Subtract 260 from 278 to get 18.
Grab the next digit (1) from the dividend, add it to 18, then carry on: 181 / 65

Advancing to step 6:
181 divided by 65 is 2 with a remainder of 51.
Use 2 as the next digit of our solution. 
Result so far: 7742.0
If we take 130 away from 181, we end up with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Moving on to step 7:
When dividing 510 by 65, we get 7 with a remainder of 55.
Put 7 as the next digit of the answer. 
Result so far: 7742.7
Subtract 455 from 510 to get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Advancing to step 8:
65 can be fit into 550 8 times, resulting in a remainder of 30.
The next digit of our result is 8. 
Result so far: 7742.78
Subtract 520 from 550 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 9:
300 divided by 65 is 4 with a remainder of 40.
The number 4 becomes the next digit in our result. 
Result so far: 7742.784
If we take 260 away from 300, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 10:
400 divided by 65 is 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 7742.7846
If we take 390 away from 400, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 11:
When dividing 100 by 65, we get 1 with a remainder of 35.
Use 1 as the next digit of our solution. 
Result so far: 7742.78461
The remainder is 35 after subtracting 65 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 12:
The number 65 fits into 350 5 times, leaving a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 7742.784615
If we subtract 325 from 350, 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.

Advancing to step 13:
65 can be fit into 250 3 times, resulting in a remainder of 55.
The next digit of our result is 3. 
Result so far: 7742.7846153
Subtracting 195 from 250 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 14:
When dividing 550 by 65, we get 8 with a remainder of 30.
Use 8 as the next digit of our solution. 
Result so far: 7742.78461538
The remainder is 30 after subtracting 520 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The quotient of the division is 7742.78461538, and the remainder is 3e-08.