8517 divided by 77 
We want to figure out the number of times 8517 can be divided by 77.

On to step 1:
When dividing 8 by 77, we get 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Take the next digit (5) from the dividend and append it to 8, then repeat: 85 / 77

Advancing to step 2:
77 goes into 85 1 times with a remainder of 8.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 77 from 85 and we're left with 8.
Append the next digit (1) from the dividend to 8 and continue with: 81 / 77

On to step 3:
77 goes into 81 1 times with a remainder of 4.
Put 1 as the next digit of the answer. 
Result so far: 11.0
If we take 77 away from 81, we end up with 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 77

Going ahead to step 4:
47 divided by 77 is 0 with a remainder of 47.
The number 0 becomes the next digit in our result. 
Result so far: 110.0
Subtract 0 from 47 to get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Step 5:
The number 77 fits into 470 6 times, leaving a remainder of 8.
Use 6 as the next digit of our solution. 
Result so far: 110.6
Subtract 462 from 470 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 6:
77 goes into 80 1 times with a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 110.61
The remainder is 3 after subtracting 77 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 7:
When dividing 30 by 77, we get 0 with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 110.61
Subtract 0 from 30 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Let's proceed to step 8:
When dividing 300 by 77, we get 3 with a remainder of 69.
The number 3 becomes the next digit in our result. 
Result so far: 110.6103
Deduct 231 from 300 and we're left with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Moving on to step 9:
690 divided by 77 is 8 with a remainder of 74.
Write down 8 as next digit of the result. 
Result so far: 110.61038
Subtract 616 from 690 to get 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Moving on to step 10:
If we divide 740 by 77, we get 9 and a remainder of 47.
The next digit of our result is 9. 
Result so far: 110.610389
The remainder is 47 after subtracting 693 from 740.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Moving on to step 11:
When dividing 470 by 77, we get 6 with a remainder of 8.
Record the quotient 6 as the next digit in the result. 
Result so far: 110.6103896
If we subtract 462 from 470, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 12:
When dividing 80 by 77, we get 1 with a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 110.61038961
If we take 77 away from 80, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The final result is 110.61038961 with a remainder of 3e-09.