We look at the division of 583966 by 87 
We want to figure out the number of times 583966 can be divided by 87.

On to step 1:
5 divided by 87 is 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (8) from the dividend to 5 and continue with: 58 / 87

Advancing to step 2:
The number 87 fits into 58 0 times, leaving a remainder of 58.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 58, we get 58.
Grab the next digit (3) from the dividend, add it to 58, then carry on: 583 / 87

Moving on to step 3:
If we divide 583 by 87, we get 6 and a remainder of 61.
The next digit of our result is 6. 
Result so far: 6.0
Deduct 522 from 583 and we're left with 61.
Fetch the next digit (9) from the dividend, attach it to 61 and continue: 619 / 87

Advancing to step 4:
619 divided by 87 is 7 with a remainder of 10.
Use 7 as the next digit of our solution. 
Result so far: 67.0
Subtract 609 from 619 to get 10.
Bring next digit (6) of the dividend behind the 10 and repeat the process: 106 / 87

Step 5:
The number 87 fits into 106 1 times, leaving a remainder of 19.
Use 1 as the next digit of our solution. 
Result so far: 671.0
Subtract 87 from 106 to get 19.
Include the next digit (6) from the dividend after 19, then repeat: 196 / 87

Going ahead to step 6:
When dividing 196 by 87, we get 2 with a remainder of 22.
Write down 2 as next digit of the result. 
Result so far: 6712.0
Subtract 174 from 196 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Moving on to step 7:
87 can be fit into 220 2 times, resulting in a remainder of 46.
The next digit of our result is 2. 
Result so far: 6712.2
Subtract 174 from 220 to get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 8:
460 divided by 87 is 5 with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 6712.25
The remainder is 25 after subtracting 435 from 460.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 9:
If we divide 250 by 87, we get 2 and a remainder of 76.
Put 2 as the next digit of the answer. 
Result so far: 6712.252
The remainder is 76 after subtracting 174 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

On to step 10:
The number 87 fits into 760 8 times, leaving a remainder of 64.
Record the quotient 8 as the next digit in the result. 
Result so far: 6712.2528
If we take 696 away from 760, we end up with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

On to step 11:
When dividing 640 by 87, we get 7 with a remainder of 31.
The number 7 becomes the next digit in our result. 
Result so far: 6712.25287
Deduct 609 from 640 and we're left with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 12:
87 can be fit into 310 3 times, resulting in a remainder of 49.
Write down 3 as next digit of the result. 
Result so far: 6712.252873
If we take 261 away from 310, we end up with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Moving on to step 13:
If we divide 490 by 87, we get 5 and a remainder of 55.
Record the quotient 5 as the next digit in the result. 
Result so far: 6712.2528735
Deduct 435 from 490 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Step 14:
If we divide 550 by 87, we get 6 and a remainder of 28.
Record the quotient 6 as the next digit in the result. 
Result so far: 6712.25287356
The remainder is 28 after subtracting 522 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

The final result is 6712.25287356 with a remainder of 2.8e-08.