64588 ÷ 6 = 10764 R4
Alright, let's work through the division of 64588 by 6 step by step.

Step 1:
6 goes into 6 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 6 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 6

Step 2:
6 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 / 6

Step 3:
6 goes into 45 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 107
Subtract 42 from 45 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 6

Step 4:
6 goes into 38 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 1076
Subtract 36 from 38 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 6

Step 5:
6 goes into 28 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 10764
Subtract 24 from 28 to get 4.

The final result is 10764 with a remainder of 4.