We look at the division of 379508 by 51 
We're looking to find how many times 51 goes into 379508.

Going ahead to step 1:
The number 51 fits into 3 0 times, leaving a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 51

Moving on to step 2:
When dividing 37 by 51, we get 0 with a remainder of 37.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Grab the next digit (9) from the dividend, add it to 37, then carry on: 379 / 51

Going ahead to step 3:
When dividing 379 by 51, we get 7 with a remainder of 22.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtract 357 from 379 to get 22.
Include the next digit (5) from the dividend after 22, then repeat: 225 / 51

Advancing to step 4:
51 can be fit into 225 4 times, resulting in a remainder of 21.
The next digit of our result is 4. 
Result so far: 74.0
The remainder is 21 after subtracting 204 from 225.
Fetch the next digit (0) from the dividend, attach it to 21 and continue: 210 / 51

Moving on to step 5:
51 can be fit into 210 4 times, resulting in a remainder of 6.
Record the quotient 4 as the next digit in the result. 
Result so far: 744.0
If we take 204 away from 210, we end up with 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 51

Let's proceed to step 6:
When dividing 68 by 51, we get 1 with a remainder of 17.
Write down 1 as next digit of the result. 
Result so far: 7441.0
Deduct 51 from 68 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Let's proceed to step 7:
170 divided by 51 is 3 with a remainder of 17.
Put 3 as the next digit of the answer. 
Result so far: 7441.3
The remainder is 17 after subtracting 153 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Going ahead to step 8:
51 can be fit into 170 3 times, resulting in a remainder of 17.
The number 3 becomes the next digit in our result. 
Result so far: 7441.33
The remainder is 17 after subtracting 153 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

After the division, we end up with 7441.33 and a remainder of 0.017.