89906 ÷ 4 = 22476 R2
Alright, let's work through the division of 89906 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 (9) of the dividend behind the 1 and repeat the process: 19 / 4

Step 3:
4 goes into 19 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 224
Subtract 16 from 19 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 4

Step 4:
4 goes into 30 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 2247
Subtract 28 from 30 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 4

Step 5:
4 goes into 26 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 22476
Subtract 24 from 26 to get 2.

The final result is 22476 with a remainder of 2.