We're dividing 125565 by 51 
We're looking to find how many times 51 goes into 125565.

Let's proceed to step 1:
The number 51 fits into 1 0 times, leaving a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Fetch the next digit (2) from the dividend, attach it to 1 and continue: 12 / 51

Going ahead to step 2:
When dividing 12 by 51, we get 0 with a remainder of 12.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 12 leaves us with 12.
Take the next digit (5) from the dividend and append it to 12, then repeat: 125 / 51

Moving on to step 3:
51 goes into 125 2 times with a remainder of 23.
The number 2 becomes the next digit in our result. 
Result so far: 2.0
Deduct 102 from 125 and we're left with 23.
Grab the next digit (5) from the dividend, add it to 23, then carry on: 235 / 51

Advancing to step 4:
235 divided by 51 is 4 with a remainder of 31.
Write down 4 as next digit of the result. 
Result so far: 24.0
If we subtract 204 from 235, we get 31.
Append the next digit (6) from the dividend to 31 and continue with: 316 / 51

Moving on to step 5:
51 goes into 316 6 times with a remainder of 10.
Put 6 as the next digit of the answer. 
Result so far: 246.0
If we take 306 away from 316, we end up with 10.
Fetch the next digit (5) from the dividend, attach it to 10 and continue: 105 / 51

Let's proceed to step 6:
51 can be fit into 105 2 times, resulting in a remainder of 3.
Record the quotient 2 as the next digit in the result. 
Result so far: 2462.0
Subtracting 102 from 105 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.

Going ahead to step 7:
30 divided by 51 is 0 with a remainder of 30.
The next digit of our result is 0. 
Result so far: 2462.0
If we take 0 away from 30, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 8:
51 goes into 300 5 times with a remainder of 45.
Write down 5 as next digit of the result. 
Result so far: 2462.05
Subtract 255 from 300 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.

Step 9:
450 divided by 51 is 8 with a remainder of 42.
Put 8 as the next digit of the answer. 
Result so far: 2462.058
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 10:
When dividing 420 by 51, we get 8 with a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 2462.0588
The remainder is 12 after subtracting 408 from 420.
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 outcome is 2462.0588, with a leftover of 0.00012.