77735977 ÷ 757 
We want to figure out the number of times 77735977 can be divided by 757.

Step 1:
The number 757 fits into 7 0 times, leaving a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 757

Moving on to step 2:
77 divided by 757 is 0 with a remainder of 77.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 77 and we're left with 77.
Append the next digit (7) from the dividend to 77 and continue with: 777 / 757

Advancing to step 3:
If we divide 777 by 757, we get 1 and a remainder of 20.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 757 from 777 and we're left with 20.
Take the next digit (3) from the dividend and append it to 20, then repeat: 203 / 757

Going ahead to step 4:
The number 757 fits into 203 0 times, leaving a remainder of 203.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
If we take 0 away from 203, we end up with 203.
Append the next digit (5) from the dividend to 203 and continue with: 2035 / 757

Going ahead to step 5:
757 goes into 2035 2 times with a remainder of 521.
Use 2 as the next digit of our solution. 
Result so far: 102.0
If we subtract 1514 from 2035, we get 521.
Include the next digit (9) from the dividend after 521, then repeat: 5219 / 757

Going ahead to step 6:
When dividing 5219 by 757, we get 6 with a remainder of 677.
The number 6 becomes the next digit in our result. 
Result so far: 1026.0
The remainder is 677 after subtracting 4542 from 5219.
Grab the next digit (7) from the dividend, add it to 677, then carry on: 6777 / 757

On to step 7:
6777 divided by 757 is 8 with a remainder of 721.
The next digit of our result is 8. 
Result so far: 10268.0
Deduct 6056 from 6777 and we're left with 721.
Append the next digit (7) from the dividend to 721 and continue with: 7217 / 757

Advancing to step 8:
If we divide 7217 by 757, we get 9 and a remainder of 404.
The number 9 becomes the next digit in our result. 
Result so far: 102689.0
Deduct 6813 from 7217 and we're left with 404.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4040, and continue the process.

Advancing to step 9:
If we divide 4040 by 757, we get 5 and a remainder of 255.
The next digit of our result is 5. 
Result so far: 102689.5
Subtract 3785 from 4040 to get 255.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2550, and continue the process.

Moving on to step 10:
2550 divided by 757 is 3 with a remainder of 279.
Use 3 as the next digit of our solution. 
Result so far: 102689.53
Deduct 2271 from 2550 and we're left with 279.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2790, and continue the process.

Step 11:
The number 757 fits into 2790 3 times, leaving a remainder of 519.
Use 3 as the next digit of our solution. 
Result so far: 102689.533
Subtracting 2271 from 2790 leaves us with 519.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5190, and continue the process.

The final result is 102689.533 with a remainder of 0.0519.