87259 ÷ 6 = 14543 R1
Alright, let's work through the division of 87259 by 6 step by step.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 6

Step 2:
6 goes into 27 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 24 from 27 to get 3.
Bring next digit (2) of the dividend behind the 3 and repeat the process: 32 / 6

Step 3:
6 goes into 32 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 145
Subtract 30 from 32 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 6

Step 4:
6 goes into 25 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 1454
Subtract 24 from 25 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 6

Step 5:
6 goes into 19 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 14543
Subtract 18 from 19 to get 1.

The final result is 14543 with a remainder of 1.