65577 ÷ 8 = 8197 R1
Let's divide 65577 by 8.

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 (5) of the dividend behind the 6 and repeat the process: 65 / 8

Step 2:
8 goes into 65 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 64 from 65 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 8

Step 3:
8 goes into 15 1 times with a remainder of 7.
Write down 1 as next digit of of the result. 
Result so far: 81
Subtract 8 from 15 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 8

Step 4:
8 goes into 77 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 819
Subtract 72 from 77 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 8

Step 5:
8 goes into 57 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 8197
Subtract 56 from 57 to get 1.

The final result is 8197 with a remainder of 1.