91588 ÷ 6 = 15264 R4
Alright, let's work through the division of 91588 by 6 step by step.

Step 1:
6 goes into 9 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 9 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 6

Step 2:
6 goes into 31 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 30 from 31 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 6

Step 3:
6 goes into 15 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 152
Subtract 12 from 15 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: 1526
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: 15264
Subtract 24 from 28 to get 4.

The final result is 15264 with a remainder of 4.