766599 ÷ 17 
We want to divide 766599 by 17.

Step 1:
If we divide 7 by 17, we get 0 and 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.
Fetch the next digit (6) from the dividend, attach it to 7 and continue: 76 / 17

Advancing to step 2:
17 can be fit into 76 4 times, resulting in a remainder of 8.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we take 68 away from 76, we end up with 8.
Grab the next digit (6) from the dividend, add it to 8, then carry on: 86 / 17

Going ahead to step 3:
86 divided by 17 is 5 with a remainder of 1.
The number 5 becomes the next digit in our result. 
Result so far: 45.0
Subtract 85 from 86 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 17

Step 4:
15 divided by 17 is 0 with a remainder of 15.
Use 0 as the next digit of our solution. 
Result so far: 450.0
Deduct 0 from 15 and we're left with 15.
Append the next digit (9) from the dividend to 15 and continue with: 159 / 17

Advancing to step 5:
17 goes into 159 9 times with a remainder of 6.
The number 9 becomes the next digit in our result. 
Result so far: 4509.0
Subtract 153 from 159 to get 6.
Take the next digit (9) from the dividend and append it to 6, then repeat: 69 / 17

On to step 6:
17 can be fit into 69 4 times, resulting in a remainder of 1.
Put 4 as the next digit of the answer. 
Result so far: 45094.0
The remainder is 1 after subtracting 68 from 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
17 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 45094.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 8:
17 can be fit into 100 5 times, resulting in a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 45094.05
Subtracting 85 from 100 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 9:
The number 17 fits into 150 8 times, leaving a remainder of 14.
Use 8 as the next digit of our solution. 
Result so far: 45094.058
Subtract 136 from 150 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 10:
When dividing 140 by 17, we get 8 with a remainder of 4.
Put 8 as the next digit of the answer. 
Result so far: 45094.0588
Subtracting 136 from 140 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

In conclusion, the division gives 45094.0588 with a balance of 4e-05.