We look at the division of 300628 by 53 
Let's see how many times 53 fits into 300628.

Advancing to step 1:
When dividing 3 by 53, we get 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Append the next digit (0) from the dividend to 3 and continue with: 30 / 53

Going ahead to step 2:
The number 53 fits into 30 0 times, leaving a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 30 leaves us with 30.
Grab the next digit (0) from the dividend, add it to 30, then carry on: 300 / 53

Step 3:
If we divide 300 by 53, we get 5 and a remainder of 35.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 265 away from 300, we end up with 35.
Append the next digit (6) from the dividend to 35 and continue with: 356 / 53

On to step 4:
356 divided by 53 is 6 with a remainder of 38.
The number 6 becomes the next digit in our result. 
Result so far: 56.0
If we take 318 away from 356, we end up with 38.
Take the next digit (2) from the dividend and append it to 38, then repeat: 382 / 53

Advancing to step 5:
53 can be fit into 382 7 times, resulting in a remainder of 11.
Write down 7 as next digit of the result. 
Result so far: 567.0
Subtract 371 from 382 to get 11.
Include the next digit (8) from the dividend after 11, then repeat: 118 / 53

Step 6:
If we divide 118 by 53, we get 2 and a remainder of 12.
Record the quotient 2 as the next digit in the result. 
Result so far: 5672.0
If we subtract 106 from 118, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Step 7:
The number 53 fits into 120 2 times, leaving a remainder of 14.
The number 2 becomes the next digit in our result. 
Result so far: 5672.2
Subtracting 106 from 120 leaves us with 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 8:
If we divide 140 by 53, we get 2 and a remainder of 34.
Put 2 as the next digit of the answer. 
Result so far: 5672.22
The remainder is 34 after subtracting 106 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

After the division, we end up with 5672.22 and a remainder of 0.034.