We look at the division of 640707 by 51 
Our goal is to divide 640707 by 51.

On to step 1:
51 can be fit into 6 0 times, resulting in a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 51

Advancing to step 2:
51 can be fit into 64 1 times, resulting in a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we take 51 away from 64, we end up with 13.
Append the next digit (0) from the dividend to 13 and continue with: 130 / 51

Advancing to step 3:
The number 51 fits into 130 2 times, leaving a remainder of 28.
Write down 2 as next digit of the result. 
Result so far: 12.0
Deduct 102 from 130 and we're left with 28.
Append the next digit (7) from the dividend to 28 and continue with: 287 / 51

On to step 4:
287 divided by 51 is 5 with a remainder of 32.
Record the quotient 5 as the next digit in the result. 
Result so far: 125.0
If we subtract 255 from 287, we get 32.
Include the next digit (0) from the dividend after 32, then repeat: 320 / 51

On to step 5:
51 goes into 320 6 times with a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 1256.0
Subtracting 306 from 320 leaves us with 14.
Fetch the next digit (7) from the dividend, attach it to 14 and continue: 147 / 51

Moving on to step 6:
51 can be fit into 147 2 times, resulting in a remainder of 45.
Write down 2 as next digit of the result. 
Result so far: 12562.0
Deduct 102 from 147 and we're left with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

On to step 7:
If we divide 450 by 51, we get 8 and a remainder of 42.
The next digit of our result is 8. 
Result so far: 12562.8
Subtract 408 from 450 to get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Going ahead to step 8:
When dividing 420 by 51, we get 8 with a remainder of 12.
Record the quotient 8 as the next digit in the result. 
Result so far: 12562.88
Deduct 408 from 420 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The quotient of the division is 12562.88, and the remainder is 0.012.