37308 ÷ 2 = 18654 R0
Alright, let's work through the division of 37308 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 (7) of the dividend behind the 1 and repeat the process: 17 / 2

Step 2:
2 goes into 17 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 18
Subtract 16 from 17 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: 186
Subtract 12 from 13 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 2

Step 4:
2 goes into 10 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 1865
Subtract 10 from 10 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 2

Step 5:
2 goes into 8 4 times with a remainder of 0.
Write down 4 as next digit of of the result. 
Result so far: 18654
Subtract 8 from 8 to get 0.

The final result is 18654 with a remainder of 0.