8641 ÷ 9 = 960 R1
We're going to perform division on 8641 with 9 as the divisor.

Step 1:
9 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 8 to get 8.
Bring next digit (6) of the dividend behind the 8 and repeat the process: 86 / 9

Step 2:
9 goes into 86 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 81 from 86 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 9

Step 3:
9 goes into 54 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 96
Subtract 54 from 54 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 9

Step 4:
9 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 960
Subtract 0 from 1 to get 1.

The final result is 960 with a remainder of 1.