559903 ÷ 84 
We're looking to find how many times 84 goes into 559903.

Let's proceed to step 1:
If we divide 5 by 84, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 84

Let's proceed to step 2:
55 divided by 84 is 0 with a remainder of 55.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 55 to get 55.
Grab the next digit (9) from the dividend, add it to 55, then carry on: 559 / 84

Advancing to step 3:
84 goes into 559 6 times with a remainder of 55.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 55 after subtracting 504 from 559.
Append the next digit (9) from the dividend to 55 and continue with: 559 / 84

Moving on to step 4:
If we divide 559 by 84, we get 6 and a remainder of 55.
Put 6 as the next digit of the answer. 
Result so far: 66.0
Subtracting 504 from 559 leaves us with 55.
Include the next digit (0) from the dividend after 55, then repeat: 550 / 84

Let's proceed to step 5:
The number 84 fits into 550 6 times, leaving a remainder of 46.
Record the quotient 6 as the next digit in the result. 
Result so far: 666.0
Subtracting 504 from 550 leaves us with 46.
Bring next digit (3) of the dividend behind the 46 and repeat the process: 463 / 84

Step 6:
84 goes into 463 5 times with a remainder of 43.
The number 5 becomes the next digit in our result. 
Result so far: 6665.0
If we take 420 away from 463, we end up with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Let's proceed to step 7:
If we divide 430 by 84, we get 5 and a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 6665.5
If we subtract 420 from 430, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 8:
84 goes into 100 1 times with a remainder of 16.
The number 1 becomes the next digit in our result. 
Result so far: 6665.51
If we subtract 84 from 100, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 9:
84 goes into 160 1 times with a remainder of 76.
Put 1 as the next digit of the answer. 
Result so far: 6665.511
Subtract 84 from 160 to get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

In conclusion, the division gives 6665.511 with a balance of 0.0076.