We're dividing 511301 by 4 
Let's see how many times 4 fits into 511301.

Advancing to step 1:
4 can be fit into 5 1 times, resulting in a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 4 from 5 and we're left with 1.
Fetch the next digit (1) from the dividend, attach it to 1 and continue: 11 / 4

Advancing to step 2:
4 goes into 11 2 times with a remainder of 3.
Put 2 as the next digit of the answer. 
Result so far: 12.0
Subtracting 8 from 11 leaves us with 3.
Take the next digit (1) from the dividend and append it to 3, then repeat: 31 / 4

On to step 3:
The number 4 fits into 31 7 times, leaving a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 127.0
Subtract 28 from 31 to get 3.
Append the next digit (3) from the dividend to 3 and continue with: 33 / 4

On to step 4:
The number 4 fits into 33 8 times, leaving a remainder of 1.
Use 8 as the next digit of our solution. 
Result so far: 1278.0
Subtracting 32 from 33 leaves us with 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 4

Advancing to step 5:
4 goes into 10 2 times with a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 12782.0
If we take 8 away from 10, we end up with 2.
Grab the next digit (1) from the dividend, add it to 2, then carry on: 21 / 4

Let's proceed to step 6:
4 can be fit into 21 5 times, resulting in a remainder of 1.
The next digit of our result is 5. 
Result so far: 127825.0
Subtract 20 from 21 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 7:
The number 4 fits into 10 2 times, leaving a remainder of 2.
Put 2 as the next digit of the answer. 
Result so far: 127825.2
If we take 8 away from 10, 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.

Step 8:
When dividing 20 by 4, we get 5 with a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 127825.25
If we take 20 away from 20, we end up with 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 9:
If we divide 0 by 4, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 127825.25
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.

Advancing to step 10:
4 can be fit into 0 0 times, resulting in a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 127825.25
Deduct 0 from 0 and we're left with 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 127825.25, and the remainder is 0.0.