35628 divided by 51 
We're looking to find how many times 51 goes into 35628.

Step 1:
When dividing 3 by 51, we get 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 51

On to step 2:
35 divided by 51 is 0 with a remainder of 35.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 35 and we're left with 35.
Append the next digit (6) from the dividend to 35 and continue with: 356 / 51

Step 3:
51 can be fit into 356 6 times, resulting in a remainder of 50.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we subtract 306 from 356, we get 50.
Bring next digit (2) of the dividend behind the 50 and repeat the process: 502 / 51

Moving on to step 4:
When dividing 502 by 51, we get 9 with a remainder of 43.
Put 9 as the next digit of the answer. 
Result so far: 69.0
Subtract 459 from 502 to get 43.
Bring next digit (8) of the dividend behind the 43 and repeat the process: 438 / 51

Advancing to step 5:
When dividing 438 by 51, we get 8 with a remainder of 30.
Record the quotient 8 as the next digit in the result. 
Result so far: 698.0
If we subtract 408 from 438, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 6:
51 can be fit into 300 5 times, resulting in a remainder of 45.
Write down 5 as next digit of the result. 
Result so far: 698.5
If we take 255 away from 300, we end up 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.

Advancing to step 7:
51 goes into 450 8 times with a remainder of 42.
Write down 8 as next digit of the result. 
Result so far: 698.58
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:
51 goes into 420 8 times with a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 698.588
Subtracting 408 from 420 leaves us 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 698.588, and the remainder is 0.0012.