89425 ÷ 4 = 22356 R1
Alright, let's work through the division of 89425 by 4 step by step.

Step 1:
4 goes into 8 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 8 from 8 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 4

Step 2:
4 goes into 9 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 22
Subtract 8 from 9 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 4

Step 3:
4 goes into 14 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 223
Subtract 12 from 14 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 4

Step 4:
4 goes into 22 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 2235
Subtract 20 from 22 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 4

Step 5:
4 goes into 25 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 22356
Subtract 24 from 25 to get 1.

The final result is 22356 with a remainder of 1.