4125684 divided by 559 
We want to figure out the number of times 4125684 can be divided by 559.

Going ahead to step 1:
559 goes into 4 0 times with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 4, we end up with 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 559

Let's proceed to step 2:
41 divided by 559 is 0 with a remainder of 41.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 41 and we're left with 41.
Append the next digit (2) from the dividend to 41 and continue with: 412 / 559

Let's proceed to step 3:
559 can be fit into 412 0 times, resulting in a remainder of 412.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 412, we end up with 412.
Append the next digit (5) from the dividend to 412 and continue with: 4125 / 559

Moving on to step 4:
The number 559 fits into 4125 7 times, leaving a remainder of 212.
Put 7 as the next digit of the answer. 
Result so far: 7.0
Subtracting 3913 from 4125 leaves us with 212.
Append the next digit (6) from the dividend to 212 and continue with: 2126 / 559

Step 5:
The number 559 fits into 2126 3 times, leaving a remainder of 449.
The number 3 becomes the next digit in our result. 
Result so far: 73.0
If we take 1677 away from 2126, we end up with 449.
Grab the next digit (8) from the dividend, add it to 449, then carry on: 4498 / 559

Let's proceed to step 6:
559 can be fit into 4498 8 times, resulting in a remainder of 26.
Put 8 as the next digit of the answer. 
Result so far: 738.0
If we take 4472 away from 4498, we end up with 26.
Take the next digit (4) from the dividend and append it to 26, then repeat: 264 / 559

On to step 7:
The number 559 fits into 264 0 times, leaving a remainder of 264.
The next digit of our result is 0. 
Result so far: 7380.0
If we take 0 away from 264, we end up with 264.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2640, and continue the process.

Advancing to step 8:
When dividing 2640 by 559, we get 4 with a remainder of 404.
The number 4 becomes the next digit in our result. 
Result so far: 7380.4
Subtract 2236 from 2640 to get 404.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4040, and continue the process.

Advancing to step 9:
The number 559 fits into 4040 7 times, leaving a remainder of 127.
Use 7 as the next digit of our solution. 
Result so far: 7380.47
If we subtract 3913 from 4040, we get 127.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1270, and continue the process.

Step 10:
The number 559 fits into 1270 2 times, leaving a remainder of 152.
Use 2 as the next digit of our solution. 
Result so far: 7380.472
If we take 1118 away from 1270, we end up with 152.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1520, and continue the process.

Step 11:
1520 divided by 559 is 2 with a remainder of 402.
Record the quotient 2 as the next digit in the result. 
Result so far: 7380.4722
Subtracting 1118 from 1520 leaves us with 402.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4020, and continue the process.

The final result is 7380.4722 with a remainder of 0.00402.