84578 ÷ 8 = 10572 R2
Alright, let's work through the division of 84578 by 8 step by step.

Step 1:
8 goes into 8 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 8 from 8 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 8

Step 2:
8 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 4 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 8

Step 3:
8 goes into 45 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 105
Subtract 40 from 45 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 8

Step 4:
8 goes into 57 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 1057
Subtract 56 from 57 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 8

Step 5:
8 goes into 18 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 10572
Subtract 16 from 18 to get 2.

The final result is 10572 with a remainder of 2.