77141 ÷ 75 
Let's see how many times 75 fits into 77141.

On 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
If we take 0 away from 7, we end up with 7.
Append the next digit (7) from the dividend to 7 and continue with: 77 / 75

Step 2:
77 divided by 75 is 1 with a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 75 from 77, we get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 75

Moving on to step 3:
When dividing 21 by 75, we get 0 with a remainder of 21.
The next digit of our result is 0. 
Result so far: 10.0
If we take 0 away from 21, we end up with 21.
Fetch the next digit (4) from the dividend, attach it to 21 and continue: 214 / 75

On to step 4:
The number 75 fits into 214 2 times, leaving a remainder of 64.
Record the quotient 2 as the next digit in the result. 
Result so far: 102.0
If we subtract 150 from 214, we get 64.
Fetch the next digit (1) from the dividend, attach it to 64 and continue: 641 / 75

Moving on to step 5:
75 can be fit into 641 8 times, resulting in a remainder of 41.
Use 8 as the next digit of our solution. 
Result so far: 1028.0
The remainder is 41 after subtracting 600 from 641.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Advancing to step 6:
75 can be fit into 410 5 times, resulting in a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 1028.5
The remainder is 35 after subtracting 375 from 410.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 7:
The number 75 fits into 350 4 times, leaving a remainder of 50.
Write down 4 as next digit of the result. 
Result so far: 1028.54
The remainder is 50 after subtracting 300 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 8:
The number 75 fits into 500 6 times, leaving a remainder of 50.
Use 6 as the next digit of our solution. 
Result so far: 1028.546
Subtracting 450 from 500 leaves us 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.

Step 9:
The number 75 fits into 500 6 times, leaving a remainder of 50.
The next digit of our result is 6. 
Result so far: 1028.5466
Deduct 450 from 500 and we're left 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.

The final result is 1028.5466 with a remainder of 0.0005.