We look at the division of 578634 by 51 
Let's see how many times 51 fits into 578634.

Advancing to step 1:
51 goes into 5 0 times with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Grab the next digit (7) from the dividend, add it to 5, then carry on: 57 / 51

Moving on to step 2:
When dividing 57 by 51, we get 1 with a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 51 from 57 to get 6.
Append the next digit (8) from the dividend to 6 and continue with: 68 / 51

Let's proceed to step 3:
51 can be fit into 68 1 times, resulting in a remainder of 17.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
The remainder is 17 after subtracting 51 from 68.
Take the next digit (6) from the dividend and append it to 17, then repeat: 176 / 51

Let's proceed to step 4:
176 divided by 51 is 3 with a remainder of 23.
The number 3 becomes the next digit in our result. 
Result so far: 113.0
Deduct 153 from 176 and we're left with 23.
Fetch the next digit (3) from the dividend, attach it to 23 and continue: 233 / 51

Step 5:
If we divide 233 by 51, we get 4 and a remainder of 29.
Record the quotient 4 as the next digit in the result. 
Result so far: 1134.0
If we take 204 away from 233, we end up with 29.
Grab the next digit (4) from the dividend, add it to 29, then carry on: 294 / 51

Moving on to step 6:
The number 51 fits into 294 5 times, leaving a remainder of 39.
Put 5 as the next digit of the answer. 
Result so far: 11345.0
Deduct 255 from 294 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Going ahead to step 7:
The number 51 fits into 390 7 times, leaving a remainder of 33.
Put 7 as the next digit of the answer. 
Result so far: 11345.7
Deduct 357 from 390 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Moving on to step 8:
When dividing 330 by 51, we get 6 with a remainder of 24.
Use 6 as the next digit of our solution. 
Result so far: 11345.76
If we subtract 306 from 330, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 9:
51 can be fit into 240 4 times, resulting in a remainder of 36.
Put 4 as the next digit of the answer. 
Result so far: 11345.764
The remainder is 36 after subtracting 204 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 10:
The number 51 fits into 360 7 times, leaving a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 11345.7647
Subtracting 357 from 360 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 11:
If we divide 30 by 51, we get 0 and a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 11345.7647
If we subtract 0 from 30, 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.

On to step 12:
The number 51 fits into 300 5 times, leaving a remainder of 45.
The number 5 becomes the next digit in our result. 
Result so far: 11345.764705
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.

Let's proceed to step 13:
51 can be fit into 450 8 times, resulting in a remainder of 42.
The next digit of our result is 8. 
Result so far: 11345.7647058
If we take 408 away from 450, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Step 14:
If we divide 420 by 51, we get 8 and a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 11345.76470588
If we take 408 away from 420, we end up 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.

After the division, we end up with 11345.76470588 and a remainder of 1.2e-08.