19508 ÷ 2 = 9754 R0
Alright, let's work through the division of 19508 by 2 step by step.

Step 1:
2 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 2

Step 2:
2 goes into 19 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 18 from 19 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 2

Step 3:
2 goes into 15 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 97
Subtract 14 from 15 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: 975
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: 9754
Subtract 8 from 8 to get 0.

The final result is 9754 with a remainder of 0.