We're dividing 125977 by 75 
We want to figure out the number of times 125977 can be divided by 75.

Step 1:
1 divided by 75 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (2) from the dividend after 1, then repeat: 12 / 75

On to step 2:
75 goes into 12 0 times 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.
Grab the next digit (5) from the dividend, add it to 12, then carry on: 125 / 75

Going ahead to step 3:
When dividing 125 by 75, we get 1 with a remainder of 50.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 75 from 125, we get 50.
Fetch the next digit (9) from the dividend, attach it to 50 and continue: 509 / 75

Going ahead to step 4:
509 divided by 75 is 6 with a remainder of 59.
Put 6 as the next digit of the answer. 
Result so far: 16.0
Subtract 450 from 509 to get 59.
Take the next digit (7) from the dividend and append it to 59, then repeat: 597 / 75

Advancing to step 5:
The number 75 fits into 597 7 times, leaving a remainder of 72.
Put 7 as the next digit of the answer. 
Result so far: 167.0
Subtract 525 from 597 to get 72.
Take the next digit (7) from the dividend and append it to 72, then repeat: 727 / 75

Advancing to step 6:
When dividing 727 by 75, we get 9 with a remainder of 52.
The next digit of our result is 9. 
Result so far: 1679.0
If we subtract 675 from 727, we get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Going ahead to step 7:
The number 75 fits into 520 6 times, leaving a remainder of 70.
The next digit of our result is 6. 
Result so far: 1679.6
Subtracting 450 from 520 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Moving on to step 8:
75 can be fit into 700 9 times, resulting in a remainder of 25.
Record the quotient 9 as the next digit in the result. 
Result so far: 1679.69
Subtract 675 from 700 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 9:
75 goes into 250 3 times with a remainder of 25.
Record the quotient 3 as the next digit in the result. 
Result so far: 1679.693
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 10:
If we divide 250 by 75, we get 3 and a remainder of 25.
The next digit of our result is 3. 
Result so far: 1679.6933
If we take 225 away from 250, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 1679.6933 with a balance of 0.00025.