420581 ÷ 53 
We're looking to find how many times 53 goes into 420581.

Advancing to step 1:
53 can be fit into 4 0 times, resulting in a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Append the next digit (2) from the dividend to 4 and continue with: 42 / 53

Let's proceed to step 2:
When dividing 42 by 53, we get 0 with a remainder of 42.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 42 after subtracting 0 from 42.
Grab the next digit (0) from the dividend, add it to 42, then carry on: 420 / 53

Advancing to step 3:
420 divided by 53 is 7 with a remainder of 49.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtracting 371 from 420 leaves us with 49.
Take the next digit (5) from the dividend and append it to 49, then repeat: 495 / 53

On to step 4:
When dividing 495 by 53, we get 9 with a remainder of 18.
The number 9 becomes the next digit in our result. 
Result so far: 79.0
Subtract 477 from 495 to get 18.
Append the next digit (8) from the dividend to 18 and continue with: 188 / 53

Advancing to step 5:
When dividing 188 by 53, we get 3 with a remainder of 29.
The next digit of our result is 3. 
Result so far: 793.0
Deduct 159 from 188 and we're left with 29.
Include the next digit (1) from the dividend after 29, then repeat: 291 / 53

On to step 6:
The number 53 fits into 291 5 times, leaving a remainder of 26.
Write down 5 as next digit of the result. 
Result so far: 7935.0
If we take 265 away from 291, we end up with 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Going ahead to step 7:
53 goes into 260 4 times with a remainder of 48.
Record the quotient 4 as the next digit in the result. 
Result so far: 7935.4
Subtracting 212 from 260 leaves us with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Step 8:
53 goes into 480 9 times with a remainder of 3.
The next digit of our result is 9. 
Result so far: 7935.49
Subtracting 477 from 480 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 9:
53 goes into 30 0 times with a remainder of 30.
The next digit of our result is 0. 
Result so far: 7935.49
The remainder is 30 after subtracting 0 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 10:
300 divided by 53 is 5 with a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 7935.4905
The remainder is 35 after subtracting 265 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 11:
53 goes into 350 6 times with a remainder of 32.
Write down 6 as next digit of the result. 
Result so far: 7935.49056
Subtracting 318 from 350 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 12:
53 goes into 320 6 times with a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 7935.490566
If we subtract 318 from 320, 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.

In conclusion, the division gives 7935.490566 with a balance of 2e-07.