We look at the division of 586777 by 3 
Our goal is to divide 586777 by 3.

Going ahead to step 1:
3 goes into 5 1 times with a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 3 away from 5, we end up with 2.
Take the next digit (8) from the dividend and append it to 2, then repeat: 28 / 3

Advancing to step 2:
When dividing 28 by 3, we get 9 with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 19.0
Subtract 27 from 28 to get 1.
Take the next digit (6) from the dividend and append it to 1, then repeat: 16 / 3

Going ahead to step 3:
If we divide 16 by 3, we get 5 and a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 195.0
If we take 15 away from 16, we end up with 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 3

Going ahead to step 4:
3 can be fit into 17 5 times, resulting in a remainder of 2.
Use 5 as the next digit of our solution. 
Result so far: 1955.0
The remainder is 2 after subtracting 15 from 17.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 3

Moving on to step 5:
When dividing 27 by 3, we get 9 with a remainder of 0.
Write down 9 as next digit of the result. 
Result so far: 19559.0
Subtracting 27 from 27 leaves us with 0.
Grab the next digit (7) from the dividend, add it to 0, then carry on: 7 / 3

Advancing to step 6:
3 can be fit into 7 2 times, resulting in a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 195592.0
If we take 6 away from 7, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 7:
When dividing 10 by 3, we get 3 with a remainder of 1.
Record the quotient 3 as the next digit in the result. 
Result so far: 195592.3
If we subtract 9 from 10, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 8:
When dividing 10 by 3, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 195592.33
The remainder is 1 after subtracting 9 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The final result is 195592.33 with a remainder of 0.001.