We're dividing 107777 by 75 
Our goal is to divide 107777 by 75.

Advancing to step 1:
1 divided by 75 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 75

Advancing to step 2:
If we divide 10 by 75, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Fetch the next digit (7) from the dividend, attach it to 10 and continue: 107 / 75

Advancing to step 3:
The number 75 fits into 107 1 times, leaving a remainder of 32.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 32 after subtracting 75 from 107.
Take the next digit (7) from the dividend and append it to 32, then repeat: 327 / 75

Step 4:
327 divided by 75 is 4 with a remainder of 27.
Record the quotient 4 as the next digit in the result. 
Result so far: 14.0
The remainder is 27 after subtracting 300 from 327.
Grab the next digit (7) from the dividend, add it to 27, then carry on: 277 / 75

Step 5:
If we divide 277 by 75, we get 3 and a remainder of 52.
The next digit of our result is 3. 
Result so far: 143.0
The remainder is 52 after subtracting 225 from 277.
Bring next digit (7) of the dividend behind the 52 and repeat the process: 527 / 75

On to step 6:
75 can be fit into 527 7 times, resulting in a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 1437.0
Subtracting 525 from 527 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 7:
The number 75 fits into 20 0 times, leaving a remainder of 20.
Put 0 as the next digit of the answer. 
Result so far: 1437.0
Subtracting 0 from 20 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 8:
200 divided by 75 is 2 with a remainder of 50.
Use 2 as the next digit of our solution. 
Result so far: 1437.02
Subtract 150 from 200 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

On to step 9:
If we divide 500 by 75, we get 6 and a remainder of 50.
Use 6 as the next digit of our solution. 
Result so far: 1437.026
If we subtract 450 from 500, we get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Let's proceed to step 10:
When dividing 500 by 75, we get 6 with a remainder of 50.
Write down 6 as next digit of the result. 
Result so far: 1437.0266
The remainder is 50 after subtracting 450 from 500.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The final result is 1437.0266 with a remainder of 0.0005.