52577 ÷ 9 = 5841 R8
Alright, let's work through the division of 52577 by 9 step by step.

Step 1:
9 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 9

Step 2:
9 goes into 52 5 times with a remainder of 7.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 45 from 52 to get 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 9

Step 3:
9 goes into 75 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 58
Subtract 72 from 75 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 4:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 584
Subtract 36 from 37 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 9

Step 5:
9 goes into 17 1 times with a remainder of 8.
Write down 1 as next digit of of the result. 
Result so far: 5841
Subtract 9 from 17 to get 8.

The final result is 5841 with a remainder of 8.