We look at the division of 77259 by 51 
We're looking to find how many times 51 goes into 77259.

On to step 1:
The number 51 fits into 7 0 times, leaving a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 51

Step 2:
51 can be fit into 77 1 times, resulting in a remainder of 26.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 51 from 77 and we're left with 26.
Take the next digit (2) from the dividend and append it to 26, then repeat: 262 / 51

Let's proceed to step 3:
51 goes into 262 5 times with a remainder of 7.
Put 5 as the next digit of the answer. 
Result so far: 15.0
Subtracting 255 from 262 leaves us with 7.
Fetch the next digit (5) from the dividend, attach it to 7 and continue: 75 / 51

Going ahead to step 4:
51 goes into 75 1 times with a remainder of 24.
Record the quotient 1 as the next digit in the result. 
Result so far: 151.0
The remainder is 24 after subtracting 51 from 75.
Append the next digit (9) from the dividend to 24 and continue with: 249 / 51

Moving on to step 5:
When dividing 249 by 51, we get 4 with a remainder of 45.
Record the quotient 4 as the next digit in the result. 
Result so far: 1514.0
Subtract 204 from 249 to get 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 6:
51 can be fit into 450 8 times, resulting in a remainder of 42.
The number 8 becomes the next digit in our result. 
Result so far: 1514.8
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.

Going ahead to step 7:
The number 51 fits into 420 8 times, leaving a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 1514.88
Subtract 408 from 420 to get 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 final result is 1514.88 with a remainder of 0.012.