6301701 ÷ 556 
We want to figure out the number of times 6301701 can be divided by 556.

On to step 1:
556 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 556

Moving on to step 2:
If we divide 63 by 556, we get 0 and a remainder of 63.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 63, we end up with 63.
Fetch the next digit (0) from the dividend, attach it to 63 and continue: 630 / 556

Moving on to step 3:
If we divide 630 by 556, we get 1 and a remainder of 74.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 74 after subtracting 556 from 630.
Grab the next digit (1) from the dividend, add it to 74, then carry on: 741 / 556

Step 4:
The number 556 fits into 741 1 times, leaving a remainder of 185.
Use 1 as the next digit of our solution. 
Result so far: 11.0
If we subtract 556 from 741, we get 185.
Include the next digit (7) from the dividend after 185, then repeat: 1857 / 556

On to step 5:
When dividing 1857 by 556, we get 3 with a remainder of 189.
Use 3 as the next digit of our solution. 
Result so far: 113.0
Deduct 1668 from 1857 and we're left with 189.
Grab the next digit (0) from the dividend, add it to 189, then carry on: 1890 / 556

Moving on to step 6:
If we divide 1890 by 556, we get 3 and a remainder of 222.
Write down 3 as next digit of the result. 
Result so far: 1133.0
Subtract 1668 from 1890 to get 222.
Grab the next digit (1) from the dividend, add it to 222, then carry on: 2221 / 556

Moving on to step 7:
2221 divided by 556 is 3 with a remainder of 553.
Use 3 as the next digit of our solution. 
Result so far: 11333.0
Subtracting 1668 from 2221 leaves us with 553.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5530, and continue the process.

Going ahead to step 8:
If we divide 5530 by 556, we get 9 and a remainder of 526.
Use 9 as the next digit of our solution. 
Result so far: 11333.9
Deduct 5004 from 5530 and we're left with 526.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5260, and continue the process.

On to step 9:
556 can be fit into 5260 9 times, resulting in a remainder of 256.
Put 9 as the next digit of the answer. 
Result so far: 11333.99
If we take 5004 away from 5260, we end up with 256.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2560, and continue the process.

The quotient of the division is 11333.99, and the remainder is 0.256.