10582 ÷ 8 = 1322 R6
Alright, let's work through the division of 10582 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 (5) of the dividend behind the 2 and repeat the process: 25 / 8

Step 3:
8 goes into 25 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 24 from 25 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 8

Step 4:
8 goes into 18 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 132
Subtract 16 from 18 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 8

Step 5:
8 goes into 22 2 times with a remainder of 6.
Write down 2 as next digit of of the result. 
Result so far: 1322
Subtract 16 from 22 to get 6.

The final result is 1322 with a remainder of 6.