We look at the division of 4211788 by 556 
Our goal is to divide 4211788 by 556.

Advancing to step 1:
4 divided by 556 is 0 with a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 556

Step 2:
556 goes into 42 0 times with a remainder of 42.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 42 leaves us with 42.
Fetch the next digit (1) from the dividend, attach it to 42 and continue: 421 / 556

Advancing to step 3:
When dividing 421 by 556, we get 0 with a remainder of 421.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 421 after subtracting 0 from 421.
Include the next digit (1) from the dividend after 421, then repeat: 4211 / 556

Step 4:
4211 divided by 556 is 7 with a remainder of 319.
Write down 7 as next digit of the result. 
Result so far: 7.0
The remainder is 319 after subtracting 3892 from 4211.
Bring next digit (7) of the dividend behind the 319 and repeat the process: 3197 / 556

On to step 5:
3197 divided by 556 is 5 with a remainder of 417.
The next digit of our result is 5. 
Result so far: 75.0
Deduct 2780 from 3197 and we're left with 417.
Fetch the next digit (8) from the dividend, attach it to 417 and continue: 4178 / 556

Advancing to step 6:
When dividing 4178 by 556, we get 7 with a remainder of 286.
The next digit of our result is 7. 
Result so far: 757.0
Subtracting 3892 from 4178 leaves us with 286.
Take the next digit (8) from the dividend and append it to 286, then repeat: 2868 / 556

Advancing to step 7:
2868 divided by 556 is 5 with a remainder of 88.
Put 5 as the next digit of the answer. 
Result so far: 7575.0
If we take 2780 away from 2868, we end up with 88.
Since there are no more digits in the dividend, we add a zero to the remainder making it 880, and continue the process.

Advancing to step 8:
556 goes into 880 1 times with a remainder of 324.
The next digit of our result is 1. 
Result so far: 7575.1
Subtracting 556 from 880 leaves us with 324.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3240, and continue the process.

Step 9:
556 goes into 3240 5 times with a remainder of 460.
The next digit of our result is 5. 
Result so far: 7575.15
Subtracting 2780 from 3240 leaves us with 460.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4600, and continue the process.

Step 10:
4600 divided by 556 is 8 with a remainder of 152.
The next digit of our result is 8. 
Result so far: 7575.158
If we subtract 4448 from 4600, we get 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:
If we divide 1520 by 556, we get 2 and a remainder of 408.
The number 2 becomes the next digit in our result. 
Result so far: 7575.1582
The remainder is 408 after subtracting 1112 from 1520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4080, and continue the process.

Going ahead to step 12:
556 goes into 4080 7 times with a remainder of 188.
Use 7 as the next digit of our solution. 
Result so far: 7575.15827
If we take 3892 away from 4080, we end up with 188.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1880, and continue the process.

Step 13:
556 can be fit into 1880 3 times, resulting in a remainder of 212.
Use 3 as the next digit of our solution. 
Result so far: 7575.158273
The remainder is 212 after subtracting 1668 from 1880.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2120, and continue the process.

Let's proceed to step 14:
556 goes into 2120 3 times with a remainder of 452.
The number 3 becomes the next digit in our result. 
Result so far: 7575.1582733
If we subtract 1668 from 2120, we get 452.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4520, and continue the process.

The final result is 7575.1582733 with a remainder of 4.52e-06.