82589 ÷ 7 = 11798 R3
Alright, let's work through the division of 82589 by 7 step by step.

Step 1:
7 goes into 8 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 8 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 7

Step 2:
7 goes into 12 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 7 from 12 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 7

Step 3:
7 goes into 55 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 117
Subtract 49 from 55 to get 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 7

Step 4:
7 goes into 68 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 1179
Subtract 63 from 68 to get 5.
Bring next digit (9) of the dividend behind the 5 and repeat the process: 59 / 7

Step 5:
7 goes into 59 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 11798
Subtract 56 from 59 to get 3.

The final result is 11798 with a remainder of 3.