771698 ÷ 75 
We want to figure out the number of times 771698 can be divided by 75.

Going ahead to step 1:
75 goes into 7 0 times with a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Include the next digit (7) from the dividend after 7, then repeat: 77 / 75

Advancing to 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.
Append the next digit (1) from the dividend to 2 and continue with: 21 / 75

Going ahead to step 3:
When dividing 21 by 75, we get 0 with a remainder of 21.
Use 0 as the next digit of our solution. 
Result so far: 10.0
Subtract 0 from 21 to get 21.
Include the next digit (6) from the dividend after 21, then repeat: 216 / 75

Advancing to step 4:
75 can be fit into 216 2 times, resulting in a remainder of 66.
Put 2 as the next digit of the answer. 
Result so far: 102.0
Deduct 150 from 216 and we're left with 66.
Grab the next digit (9) from the dividend, add it to 66, then carry on: 669 / 75

Step 5:
669 divided by 75 is 8 with a remainder of 69.
The next digit of our result is 8. 
Result so far: 1028.0
Subtracting 600 from 669 leaves us with 69.
Bring next digit (8) of the dividend behind the 69 and repeat the process: 698 / 75

Moving on to step 6:
75 can be fit into 698 9 times, resulting in a remainder of 23.
Use 9 as the next digit of our solution. 
Result so far: 10289.0
Subtracting 675 from 698 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 7:
The number 75 fits into 230 3 times, leaving a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 10289.3
If we take 225 away from 230, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
50 divided by 75 is 0 with a remainder of 50.
Put 0 as the next digit of the answer. 
Result so far: 10289.3
If we take 0 away from 50, 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 9:
If we divide 500 by 75, we get 6 and a remainder of 50.
Put 6 as the next digit of the answer. 
Result so far: 10289.306
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.

On 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: 10289.3066
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.

The quotient of the division is 10289.3066, and the remainder is 0.0005.