83677 ÷ 8 = 10459 R5
Alright, let's work through the division of 83677 by 8 step by step.

Step 1:
8 goes into 8 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 8 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 8

Step 2:
8 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 3 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 8

Step 3:
8 goes into 36 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 104
Subtract 32 from 36 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 8

Step 4:
8 goes into 47 5 times with a remainder of 7.
Write down 5 as next digit of of the result. 
Result so far: 1045
Subtract 40 from 47 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 8

Step 5:
8 goes into 77 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 10459
Subtract 72 from 77 to get 5.

The final result is 10459 with a remainder of 5.