77514 ÷ 9 = 8612 R6
Alright, let's work through the division of 77514 by 9 step by step.

Step 1:
9 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 7 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 9

Step 2:
9 goes into 77 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 72 from 77 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 9

Step 3:
9 goes into 55 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 86
Subtract 54 from 55 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 9

Step 4:
9 goes into 11 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 861
Subtract 9 from 11 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 9

Step 5:
9 goes into 24 2 times with a remainder of 6.
Write down 2 as next digit of of the result. 
Result so far: 8612
Subtract 18 from 24 to get 6.

The final result is 8612 with a remainder of 6.