66306 ÷ 4 = 16576 R2
Alright, let's work through the division of 66306 by 4 step by step.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 4

Step 2:
4 goes into 26 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 24 from 26 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 4

Step 3:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 165
Subtract 20 from 23 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: 1657
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: 16576
Subtract 24 from 26 to get 2.

The final result is 16576 with a remainder of 2.