25537 ÷ 6 = 4256 R1
Alright, let's work through the division of 25537 by 6 step by step.

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 (3) of the dividend behind the 3 and repeat the process: 33 / 6

Step 4:
6 goes into 33 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 425
Subtract 30 from 33 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 6

Step 5:
6 goes into 37 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 4256
Subtract 36 from 37 to get 1.

The final result is 4256 with a remainder of 1.