9561 ÷ 8 = 1195 R1
Alright, let's work through the division of 9561 by 8 step by step.

Step 1:
8 goes into 9 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 9 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 8

Step 2:
8 goes into 15 1 times with a remainder of 7.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 8 from 15 to get 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 8

Step 3:
8 goes into 76 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 119
Subtract 72 from 76 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 8

Step 4:
8 goes into 41 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 1195
Subtract 40 from 41 to get 1.

The final result is 1195 with a remainder of 1.