We're dividing 3585066 by 584 
We're looking to find how many times 584 goes into 3585066.

On to step 1:
When dividing 3 by 584, we get 0 with a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 584

Step 2:
584 goes into 35 0 times with a remainder of 35.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 35 to get 35.
Include the next digit (8) from the dividend after 35, then repeat: 358 / 584

Going ahead to step 3:
584 can be fit into 358 0 times, resulting in a remainder of 358.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 358, we get 358.
Include the next digit (5) from the dividend after 358, then repeat: 3585 / 584

On to step 4:
If we divide 3585 by 584, we get 6 and a remainder of 81.
The next digit of our result is 6. 
Result so far: 6.0
Subtracting 3504 from 3585 leaves us with 81.
Include the next digit (0) from the dividend after 81, then repeat: 810 / 584

Advancing to step 5:
If we divide 810 by 584, we get 1 and a remainder of 226.
Record the quotient 1 as the next digit in the result. 
Result so far: 61.0
If we subtract 584 from 810, we get 226.
Grab the next digit (6) from the dividend, add it to 226, then carry on: 2266 / 584

On to step 6:
If we divide 2266 by 584, we get 3 and a remainder of 514.
The number 3 becomes the next digit in our result. 
Result so far: 613.0
The remainder is 514 after subtracting 1752 from 2266.
Grab the next digit (6) from the dividend, add it to 514, then carry on: 5146 / 584

On to step 7:
When dividing 5146 by 584, we get 8 with a remainder of 474.
Write down 8 as next digit of the result. 
Result so far: 6138.0
Deduct 4672 from 5146 and we're left with 474.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4740, and continue the process.

Step 8:
The number 584 fits into 4740 8 times, leaving a remainder of 68.
Use 8 as the next digit of our solution. 
Result so far: 6138.8
Deduct 4672 from 4740 and we're left with 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Moving on to step 9:
If we divide 680 by 584, we get 1 and a remainder of 96.
The number 1 becomes the next digit in our result. 
Result so far: 6138.81
Subtract 584 from 680 to get 96.
Since there are no more digits in the dividend, we add a zero to the remainder making it 960, and continue the process.

On to step 10:
When dividing 960 by 584, we get 1 with a remainder of 376.
Record the quotient 1 as the next digit in the result. 
Result so far: 6138.811
If we subtract 584 from 960, we get 376.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3760, and continue the process.

The quotient of the division is 6138.811, and the remainder is 0.0376.