95089 ÷ 6 = 15848 R1
Alright, let's work through the division of 95089 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 (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 2:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 30 from 35 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 6

Step 3:
6 goes into 50 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 158
Subtract 48 from 50 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 6

Step 4:
6 goes into 28 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 1584
Subtract 24 from 28 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 6

Step 5:
6 goes into 49 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 15848
Subtract 48 from 49 to get 1.

The final result is 15848 with a remainder of 1.