10766 ÷ 8 = 1345 R6
No problem, we've got 10766 and 8 for the division.

Step 1:
8 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 8

Step 2:
8 goes into 10 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 10 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 8

Step 3:
8 goes into 27 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 24 from 27 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 8

Step 4:
8 goes into 36 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 134
Subtract 32 from 36 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 8

Step 5:
8 goes into 46 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 1345
Subtract 40 from 46 to get 6.

The final result is 1345 with a remainder of 6.