We look at the division of 4330584 by 872 
We're looking to find how many times 872 goes into 4330584.

Moving on to step 1:
872 can be fit into 4 0 times, resulting in a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 872

Advancing to step 2:
872 goes into 43 0 times with a remainder of 43.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 43 after subtracting 0 from 43.
Append the next digit (3) from the dividend to 43 and continue with: 433 / 872

Going ahead to step 3:
872 can be fit into 433 0 times, resulting in a remainder of 433.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 433, we end up with 433.
Grab the next digit (0) from the dividend, add it to 433, then carry on: 4330 / 872

Going ahead to step 4:
872 can be fit into 4330 4 times, resulting in a remainder of 842.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Subtract 3488 from 4330 to get 842.
Include the next digit (5) from the dividend after 842, then repeat: 8425 / 872

Moving on to step 5:
8425 divided by 872 is 9 with a remainder of 577.
Write down 9 as next digit of the result. 
Result so far: 49.0
Deduct 7848 from 8425 and we're left with 577.
Append the next digit (8) from the dividend to 577 and continue with: 5778 / 872

Let's proceed to step 6:
When dividing 5778 by 872, we get 6 with a remainder of 546.
Use 6 as the next digit of our solution. 
Result so far: 496.0
The remainder is 546 after subtracting 5232 from 5778.
Take the next digit (4) from the dividend and append it to 546, then repeat: 5464 / 872

Going ahead to step 7:
5464 divided by 872 is 6 with a remainder of 232.
Write down 6 as next digit of the result. 
Result so far: 4966.0
If we subtract 5232 from 5464, we get 232.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2320, and continue the process.

Let's proceed to step 8:
872 can be fit into 2320 2 times, resulting in a remainder of 576.
Put 2 as the next digit of the answer. 
Result so far: 4966.2
If we take 1744 away from 2320, we end up with 576.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5760, and continue the process.

Let's proceed to step 9:
The number 872 fits into 5760 6 times, leaving a remainder of 528.
The next digit of our result is 6. 
Result so far: 4966.26
The remainder is 528 after subtracting 5232 from 5760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5280, and continue the process.

Moving on to step 10:
872 goes into 5280 6 times with a remainder of 48.
Record the quotient 6 as the next digit in the result. 
Result so far: 4966.266
If we take 5232 away from 5280, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

In conclusion, the division gives 4966.266 with a balance of 0.0048.