25180 ÷ 6 = 4196 R4
Alright, let's work through the division of 25180 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 (1) of the dividend behind the 1 and repeat the process: 11 / 6

Step 3:
6 goes into 11 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 41
Subtract 6 from 11 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 6

Step 4:
6 goes into 58 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 419
Subtract 54 from 58 to get 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 6

Step 5:
6 goes into 40 6 times with a remainder of 4.
Write down 6 as next digit of of the result. 
Result so far: 4196
Subtract 36 from 40 to get 4.

The final result is 4196 with a remainder of 4.