64677 ÷ 8 = 8084 R5
Alright, let's work through the division of 64677 by 8 step by step.

Step 1:
8 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 8

Step 2:
8 goes into 64 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 64 from 64 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 8

Step 3:
8 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 80
Subtract 0 from 6 to get 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 8

Step 4:
8 goes into 67 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 808
Subtract 64 from 67 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 8

Step 5:
8 goes into 37 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 8084
Subtract 32 from 37 to get 5.

The final result is 8084 with a remainder of 5.