We're dividing 42577 by 53 
Our goal is to divide 42577 by 53.

Let's proceed to step 1:
If we divide 4 by 53, we get 0 and a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 53

Moving on to step 2:
53 goes into 42 0 times with a remainder of 42.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 42 to get 42.
Grab the next digit (5) from the dividend, add it to 42, then carry on: 425 / 53

Step 3:
53 goes into 425 8 times with a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 8.0
The remainder is 1 after subtracting 424 from 425.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 53

Let's proceed to step 4:
If we divide 17 by 53, we get 0 and a remainder of 17.
Use 0 as the next digit of our solution. 
Result so far: 80.0
If we subtract 0 from 17, we get 17.
Include the next digit (7) from the dividend after 17, then repeat: 177 / 53

On to step 5:
If we divide 177 by 53, we get 3 and a remainder of 18.
Put 3 as the next digit of the answer. 
Result so far: 803.0
Subtract 159 from 177 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 6:
The number 53 fits into 180 3 times, leaving a remainder of 21.
The next digit of our result is 3. 
Result so far: 803.3
If we subtract 159 from 180, we get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Moving on to step 7:
210 divided by 53 is 3 with a remainder of 51.
Record the quotient 3 as the next digit in the result. 
Result so far: 803.33
Deduct 159 from 210 and we're left 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.

After the division, we end up with 803.33 and a remainder of 0.051.