13577 ÷ 9 = 1508 R5
Let's divide 13577 by 9.

Step 1:
9 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 9

Step 2:
9 goes into 13 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 9 from 13 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 9

Step 3:
9 goes into 45 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 45 from 45 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 9

Step 4:
9 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 150
Subtract 0 from 7 to get 7.
Bring next digit (7) of the dividend behind the 7 and repeat the process: 77 / 9

Step 5:
9 goes into 77 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 1508
Subtract 72 from 77 to get 5.

The final result is 1508 with a remainder of 5.