89372 ÷ 8 = 11171 R4
Alright, let's work through the division of 89372 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 (9) of the dividend behind the 0 and repeat the process: 9 / 8

Step 2:
8 goes into 9 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 8 from 9 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 8

Step 3:
8 goes into 13 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 111
Subtract 8 from 13 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: 1117
Subtract 56 from 57 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 8

Step 5:
8 goes into 12 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 11171
Subtract 8 from 12 to get 4.

The final result is 11171 with a remainder of 4.