We look at the division of 512041 by 59 
Our goal is to divide 512041 by 59.

Moving on to step 1:
When dividing 5 by 59, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 59

On to step 2:
51 divided by 59 is 0 with a remainder of 51.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 51, we end up with 51.
Fetch the next digit (2) from the dividend, attach it to 51 and continue: 512 / 59

Step 3:
When dividing 512 by 59, we get 8 with a remainder of 40.
The next digit of our result is 8. 
Result so far: 8.0
If we subtract 472 from 512, we get 40.
Bring next digit (0) of the dividend behind the 40 and repeat the process: 400 / 59

Going ahead to step 4:
If we divide 400 by 59, we get 6 and a remainder of 46.
Use 6 as the next digit of our solution. 
Result so far: 86.0
The remainder is 46 after subtracting 354 from 400.
Append the next digit (4) from the dividend to 46 and continue with: 464 / 59

Moving on to step 5:
464 divided by 59 is 7 with a remainder of 51.
Write down 7 as next digit of the result. 
Result so far: 867.0
The remainder is 51 after subtracting 413 from 464.
Bring next digit (1) of the dividend behind the 51 and repeat the process: 511 / 59

Moving on to step 6:
The number 59 fits into 511 8 times, leaving a remainder of 39.
Write down 8 as next digit of the result. 
Result so far: 8678.0
The remainder is 39 after subtracting 472 from 511.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Let's proceed to step 7:
59 can be fit into 390 6 times, resulting in a remainder of 36.
Write down 6 as next digit of the result. 
Result so far: 8678.6
Subtract 354 from 390 to get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 8:
The number 59 fits into 360 6 times, leaving a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 8678.66
Deduct 354 from 360 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

After the division, we end up with 8678.66 and a remainder of 0.006.