25586 ÷ 6 = 4264 R2
We're going to perform division on 25586 with 6 as the divisor.

Step 1:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 6

Step 2:
6 goes into 25 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 24 from 25 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: 42
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: 426
Subtract 36 from 38 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 6

Step 5:
6 goes into 26 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 4264
Subtract 24 from 26 to get 2.

The final result is 4264 with a remainder of 2.