31584 ÷ 2 = 15792 R0
Alright, let's work through the division of 31584 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 (1) of the dividend behind the 1 and repeat the process: 11 / 2

Step 2:
2 goes into 11 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 10 from 11 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: 157
Subtract 14 from 15 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 2

Step 4:
2 goes into 18 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 1579
Subtract 18 from 18 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 2

Step 5:
2 goes into 4 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 15792
Subtract 4 from 4 to get 0.

The final result is 15792 with a remainder of 0.