57609 ÷ 8 = 7201 R1
Alright, let's work through the division of 57609 by 8 step by step.

Step 1:
8 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 8

Step 2:
8 goes into 57 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 56 from 57 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 8

Step 3:
8 goes into 16 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 72
Subtract 16 from 16 to get 0.
Bring next digit (0) of the dividend behind the 0 and repeat the process: 0 / 8

Step 4:
8 goes into 0 0 times with a remainder of 0.
Write down 0 as next digit of of the result. 
Result so far: 720
Subtract 0 from 0 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 8

Step 5:
8 goes into 9 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 7201
Subtract 8 from 9 to get 1.

The final result is 7201 with a remainder of 1.