57509 ÷ 6 = 9584 R5
Alright, let's work through the division of 57509 by 6 step by step.

Step 1:
6 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 / 6

Step 2:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 54 from 57 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 3:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 95
Subtract 30 from 35 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 6

Step 4:
6 goes into 50 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 958
Subtract 48 from 50 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 6

Step 5:
6 goes into 29 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 9584
Subtract 24 from 29 to get 5.

The final result is 9584 with a remainder of 5.