585741 ÷ 51 
Our goal is to divide 585741 by 51.

Moving on to step 1:
When dividing 5 by 51, we get 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 51

Let's proceed to step 2:
The number 51 fits into 58 1 times, leaving a remainder of 7.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 51 from 58 to get 7.
Include the next digit (5) from the dividend after 7, then repeat: 75 / 51

Step 3:
75 divided by 51 is 1 with a remainder of 24.
Put 1 as the next digit of the answer. 
Result so far: 11.0
If we take 51 away from 75, we end up with 24.
Take the next digit (7) from the dividend and append it to 24, then repeat: 247 / 51

Moving on to step 4:
51 can be fit into 247 4 times, resulting in a remainder of 43.
The next digit of our result is 4. 
Result so far: 114.0
If we take 204 away from 247, we end up with 43.
Bring next digit (4) of the dividend behind the 43 and repeat the process: 434 / 51

Going ahead to step 5:
434 divided by 51 is 8 with a remainder of 26.
Put 8 as the next digit of the answer. 
Result so far: 1148.0
Deduct 408 from 434 and we're left with 26.
Include the next digit (1) from the dividend after 26, then repeat: 261 / 51

Advancing to step 6:
If we divide 261 by 51, we get 5 and a remainder of 6.
Write down 5 as next digit of the result. 
Result so far: 11485.0
Deduct 255 from 261 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.

Going ahead to step 7:
60 divided by 51 is 1 with a remainder of 9.
Use 1 as the next digit of our solution. 
Result so far: 11485.1
Subtracting 51 from 60 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 8:
51 goes into 90 1 times with a remainder of 39.
Put 1 as the next digit of the answer. 
Result so far: 11485.11
Subtract 51 from 90 to get 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

After the division, we end up with 11485.11 and a remainder of 0.039.