33377 ÷ 2 = 16688 R1
Alright, let's work through the division of 33377 by 2 step by step.

Step 1:
2 goes into 3 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 2 from 3 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 2

Step 2:
2 goes into 13 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 12 from 13 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 2

Step 3:
2 goes into 13 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 166
Subtract 12 from 13 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 2

Step 4:
2 goes into 17 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 1668
Subtract 16 from 17 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 2

Step 5:
2 goes into 17 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 16688
Subtract 16 from 17 to get 1.

The final result is 16688 with a remainder of 1.