19574 ÷ 2 = 9787 R0
Alright, let's work through the division of 19574 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 (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: 978
Subtract 16 from 17 to get 1.
Bring next digit (4) of the dividend behind the 1 and repeat the process: 14 / 2

Step 5:
2 goes into 14 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 9787
Subtract 14 from 14 to get 0.

The final result is 9787 with a remainder of 0.