10633 ÷ 8 = 1329 R1
Alright, let's work through the division of 10633 by 8 step by step.

Step 1:
8 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 (0) of the dividend behind the 1 and repeat the process: 10 / 8

Step 2:
8 goes into 10 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 10 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 8

Step 3:
8 goes into 26 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 24 from 26 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 8

Step 4:
8 goes into 23 2 times with a remainder of 7.
Write down 2 as next digit of of the result. 
Result so far: 132
Subtract 16 from 23 to get 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 8

Step 5:
8 goes into 73 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 1329
Subtract 72 from 73 to get 1.

The final result is 1329 with a remainder of 1.