6089 ÷ 7 = 869 R6
Alright, let's work through the division of 6089 by 7 step by step.

Step 1:
7 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (0) of the dividend behind the 6 and repeat the process: 60 / 7

Step 2:
7 goes into 60 8 times with a remainder of 4.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 56 from 60 to get 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 7

Step 3:
7 goes into 48 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 86
Subtract 42 from 48 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 7

Step 4:
7 goes into 69 9 times with a remainder of 6.
Write down 9 as next digit of of the result. 
Result so far: 869
Subtract 63 from 69 to get 6.

The final result is 869 with a remainder of 6.