We look at the division of 557341 by 53 
We want to figure out the number of times 557341 can be divided by 53.

Going ahead to step 1:
53 goes into 5 0 times with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (5) from the dividend to 5 and continue with: 55 / 53

Going ahead to step 2:
53 can be fit into 55 1 times, resulting in a remainder of 2.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 53 from 55 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 53

Going ahead to step 3:
53 can be fit into 27 0 times, resulting in a remainder of 27.
Write down 0 as next digit of the result. 
Result so far: 10.0
Deduct 0 from 27 and we're left with 27.
Take the next digit (3) from the dividend and append it to 27, then repeat: 273 / 53

Moving on to step 4:
The number 53 fits into 273 5 times, leaving a remainder of 8.
The number 5 becomes the next digit in our result. 
Result so far: 105.0
If we subtract 265 from 273, we get 8.
Include the next digit (4) from the dividend after 8, then repeat: 84 / 53

Let's proceed to step 5:
84 divided by 53 is 1 with a remainder of 31.
The next digit of our result is 1. 
Result so far: 1051.0
The remainder is 31 after subtracting 53 from 84.
Take the next digit (1) from the dividend and append it to 31, then repeat: 311 / 53

Step 6:
The number 53 fits into 311 5 times, leaving a remainder of 46.
The number 5 becomes the next digit in our result. 
Result so far: 10515.0
If we take 265 away from 311, we end up with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 7:
53 can be fit into 460 8 times, resulting in a remainder of 36.
The next digit of our result is 8. 
Result so far: 10515.8
If we take 424 away from 460, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Let's proceed to step 8:
If we divide 360 by 53, we get 6 and a remainder of 42.
Put 6 as the next digit of the answer. 
Result so far: 10515.86
The remainder is 42 after subtracting 318 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 9:
When dividing 420 by 53, we get 7 with a remainder of 49.
Write down 7 as next digit of the result. 
Result so far: 10515.867
If we take 371 away from 420, we end up with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Going ahead to step 10:
53 can be fit into 490 9 times, resulting in a remainder of 13.
Write down 9 as next digit of the result. 
Result so far: 10515.8679
Subtracting 477 from 490 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Going ahead to step 11:
When dividing 130 by 53, we get 2 with a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 10515.86792
Deduct 106 from 130 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 12:
240 divided by 53 is 4 with a remainder of 28.
Record the quotient 4 as the next digit in the result. 
Result so far: 10515.867924
The remainder is 28 after subtracting 212 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 13:
280 divided by 53 is 5 with a remainder of 15.
Put 5 as the next digit of the answer. 
Result so far: 10515.8679245
If we take 265 away from 280, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Step 14:
If we divide 150 by 53, we get 2 and a remainder of 44.
Put 2 as the next digit of the answer. 
Result so far: 10515.86792452
Deduct 106 from 150 and we're left with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

The final outcome is 10515.86792452, with a leftover of 4.4e-08.