66109 ÷ 4 = 16527 R1
Alright, let's work through the division of 66109 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 (1) of the dividend behind the 2 and repeat the process: 21 / 4

Step 3:
4 goes into 21 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 165
Subtract 20 from 21 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 4

Step 4:
4 goes into 10 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 1652
Subtract 8 from 10 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 4

Step 5:
4 goes into 29 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 16527
Subtract 28 from 29 to get 1.

The final result is 16527 with a remainder of 1.