36665 ÷ 8 = 4583 R1
Alright, let's work through the division of 36665 by 8 step by step.

Step 1:
8 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 8

Step 2:
8 goes into 36 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 32 from 36 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 8

Step 3:
8 goes into 46 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 45
Subtract 40 from 46 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 8

Step 4:
8 goes into 66 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 458
Subtract 64 from 66 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 8

Step 5:
8 goes into 25 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 4583
Subtract 24 from 25 to get 1.

The final result is 4583 with a remainder of 1.