577506 ÷ 42 
We're looking to find how many times 42 goes into 577506.

On to step 1:
The number 42 fits into 5 0 times, leaving a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Take the next digit (7) from the dividend and append it to 5, then repeat: 57 / 42

Going ahead to step 2:
42 goes into 57 1 times with a remainder of 15.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtracting 42 from 57 leaves us with 15.
Append the next digit (7) from the dividend to 15 and continue with: 157 / 42

On to step 3:
157 divided by 42 is 3 with a remainder of 31.
Use 3 as the next digit of our solution. 
Result so far: 13.0
Subtract 126 from 157 to get 31.
Append the next digit (5) from the dividend to 31 and continue with: 315 / 42

Moving on to step 4:
315 divided by 42 is 7 with a remainder of 21.
The next digit of our result is 7. 
Result so far: 137.0
If we take 294 away from 315, we end up with 21.
Append the next digit (0) from the dividend to 21 and continue with: 210 / 42

Advancing to step 5:
42 goes into 210 5 times with a remainder of 0.
The number 5 becomes the next digit in our result. 
Result so far: 1375.0
The remainder is 0 after subtracting 210 from 210.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 42

Step 6:
The number 42 fits into 6 0 times, leaving a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 13750.0
Subtract 0 from 6 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 7:
42 goes into 60 1 times with a remainder of 18.
Put 1 as the next digit of the answer. 
Result so far: 13750.1
If we subtract 42 from 60, we 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.

Moving on to step 8:
When dividing 180 by 42, we get 4 with a remainder of 12.
Record the quotient 4 as the next digit in the result. 
Result so far: 13750.14
The remainder is 12 after subtracting 168 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 9:
120 divided by 42 is 2 with a remainder of 36.
Write down 2 as next digit of the result. 
Result so far: 13750.142
If we take 84 away from 120, 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 10:
The number 42 fits into 360 8 times, leaving a remainder of 24.
The number 8 becomes the next digit in our result. 
Result so far: 13750.1428
If we subtract 336 from 360, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Step 11:
240 divided by 42 is 5 with a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 13750.14285
Subtracting 210 from 240 leaves us with 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 12:
300 divided by 42 is 7 with a remainder of 6.
The next digit of our result is 7. 
Result so far: 13750.142857
If we subtract 294 from 300, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 13:
42 can be fit into 60 1 times, resulting in a remainder of 18.
Record the quotient 1 as the next digit in the result. 
Result so far: 13750.1428571
If we take 42 away from 60, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 14:
42 goes into 180 4 times with a remainder of 12.
The number 4 becomes the next digit in our result. 
Result so far: 13750.14285714
Subtract 168 from 180 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 13750.14285714 with a balance of 1.2e-08.