7787 ÷ 75 
Our goal is to divide 7787 by 75.

Let's proceed to step 1:
75 can be fit into 7 0 times, resulting in a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 7 leaves us with 7.
Fetch the next digit (7) from the dividend, attach it to 7 and continue: 77 / 75

Step 2:
When dividing 77 by 75, we get 1 with a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Deduct 75 from 77 and we're left with 2.
Take the next digit (8) from the dividend and append it to 2, then repeat: 28 / 75

Advancing to step 3:
When dividing 28 by 75, we get 0 with a remainder of 28.
The next digit of our result is 0. 
Result so far: 10.0
The remainder is 28 after subtracting 0 from 28.
Fetch the next digit (7) from the dividend, attach it to 28 and continue: 287 / 75

On to step 4:
75 goes into 287 3 times with a remainder of 62.
Put 3 as the next digit of the answer. 
Result so far: 103.0
If we subtract 225 from 287, we get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Advancing to step 5:
If we divide 620 by 75, we get 8 and a remainder of 20.
Record the quotient 8 as the next digit in the result. 
Result so far: 103.8
If we take 600 away from 620, we end up 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.

Going ahead to step 6:
If we divide 200 by 75, we get 2 and a remainder of 50.
The number 2 becomes the next digit in our result. 
Result so far: 103.82
If we take 150 away from 200, we end up with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Advancing to step 7:
75 goes into 500 6 times with a remainder of 50.
The number 6 becomes the next digit in our result. 
Result so far: 103.826
Subtract 450 from 500 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 8:
75 goes into 500 6 times with a remainder of 50.
The next digit of our result is 6. 
Result so far: 103.8266
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 103.8266 with a remainder of 0.0005.