66049 ÷ 4 = 16512 R1
Alright, let's work through the division of 66049 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 (0) of the dividend behind the 2 and repeat the process: 20 / 4

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

Step 4:
4 goes into 4 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1651
Subtract 4 from 4 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 4

Step 5:
4 goes into 9 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 16512
Subtract 8 from 9 to get 1.

The final result is 16512 with a remainder of 1.