25812 ÷ 7 = 3687 R3
Alright, let's work through the division of 25812 by 7 step by step.

Step 1:
7 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 / 7

Step 2:
7 goes into 25 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 21 from 25 to get 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 7

Step 3:
7 goes into 48 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 36
Subtract 42 from 48 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 7

Step 4:
7 goes into 61 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 368
Subtract 56 from 61 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 7

Step 5:
7 goes into 52 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 3687
Subtract 49 from 52 to get 3.

The final result is 3687 with a remainder of 3.