We look at the division of 51377 by 34 
Let's see how many times 34 fits into 51377.

Moving on to step 1:
34 goes into 5 0 times with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 34

On to step 2:
When dividing 51 by 34, we get 1 with a remainder of 17.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 34 from 51 and we're left with 17.
Fetch the next digit (3) from the dividend, attach it to 17 and continue: 173 / 34

Let's proceed to step 3:
The number 34 fits into 173 5 times, leaving a remainder of 3.
Record the quotient 5 as the next digit in the result. 
Result so far: 15.0
The remainder is 3 after subtracting 170 from 173.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 34

Let's proceed to step 4:
The number 34 fits into 37 1 times, leaving a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 151.0
If we subtract 34 from 37, we get 3.
Grab the next digit (7) from the dividend, add it to 3, then carry on: 37 / 34

Step 5:
If we divide 37 by 34, we get 1 and a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 1511.0
Deduct 34 from 37 and we're left 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.

Going ahead to step 6:
34 can be fit into 30 0 times, resulting in a remainder of 30.
Record the quotient 0 as the next digit in the result. 
Result so far: 1511.0
Subtract 0 from 30 to 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 7:
If we divide 300 by 34, we get 8 and a remainder of 28.
The next digit of our result is 8. 
Result so far: 1511.08
If we take 272 away from 300, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 8:
34 can be fit into 280 8 times, resulting in a remainder of 8.
Use 8 as the next digit of our solution. 
Result so far: 1511.088
Subtract 272 from 280 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

In conclusion, the division gives 1511.088 with a balance of 0.0008.