We look at the division of 577313 by 42 
We want to figure out the number of times 577313 can be divided by 42.

Step 1:
42 can be fit into 5 0 times, resulting in a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (7) from the dividend after 5, then repeat: 57 / 42

Moving on to step 2:
The number 42 fits into 57 1 times, leaving a remainder of 15.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 42 from 57 to get 15.
Bring next digit (7) of the dividend behind the 15 and repeat the process: 157 / 42

Advancing to step 3:
42 can be fit into 157 3 times, resulting in a remainder of 31.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Deduct 126 from 157 and we're left with 31.
Append the next digit (3) from the dividend to 31 and continue with: 313 / 42

On to step 4:
If we divide 313 by 42, we get 7 and a remainder of 19.
Write down 7 as next digit of the result. 
Result so far: 137.0
The remainder is 19 after subtracting 294 from 313.
Bring next digit (1) of the dividend behind the 19 and repeat the process: 191 / 42

Step 5:
42 goes into 191 4 times with a remainder of 23.
Put 4 as the next digit of the answer. 
Result so far: 1374.0
Subtract 168 from 191 to get 23.
Fetch the next digit (3) from the dividend, attach it to 23 and continue: 233 / 42

Advancing to step 6:
42 goes into 233 5 times with a remainder of 23.
The number 5 becomes the next digit in our result. 
Result so far: 13745.0
If we take 210 away from 233, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 7:
42 goes into 230 5 times with a remainder of 20.
Write down 5 as next digit of the result. 
Result so far: 13745.5
Subtracting 210 from 230 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 8:
42 goes into 200 4 times with a remainder of 32.
Record the quotient 4 as the next digit in the result. 
Result so far: 13745.54
Subtracting 168 from 200 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.

Going ahead to step 9:
The number 42 fits into 320 7 times, leaving a remainder of 26.
Put 7 as the next digit of the answer. 
Result so far: 13745.547
If we take 294 away from 320, 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 10:
260 divided by 42 is 6 with a remainder of 8.
Write down 6 as next digit of the result. 
Result so far: 13745.5476
Subtract 252 from 260 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 11:
80 divided by 42 is 1 with a remainder of 38.
Put 1 as the next digit of the answer. 
Result so far: 13745.54761
If we take 42 away from 80, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Let's proceed to step 12:
42 goes into 380 9 times with a remainder of 2.
The number 9 becomes the next digit in our result. 
Result so far: 13745.547619
If we subtract 378 from 380, 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.

Step 13:
42 can be fit into 20 0 times, resulting in a remainder of 20.
Use 0 as the next digit of our solution. 
Result so far: 13745.547619
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 14:
42 goes into 200 4 times with a remainder of 32.
Put 4 as the next digit of the answer. 
Result so far: 13745.54761904
If we take 168 away from 200, we end up 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.

In conclusion, the division gives 13745.54761904 with a balance of 3.2e-08.