42567 ÷ 2 = 21283 R1
Alright, let's work through the division of 42567 by 2 step by step.

Step 1:
2 goes into 4 2 times with a remainder of 0.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 4 from 4 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 2

Step 2:
2 goes into 2 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 21
Subtract 2 from 2 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 2

Step 3:
2 goes into 5 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 212
Subtract 4 from 5 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 2

Step 4:
2 goes into 16 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 2128
Subtract 16 from 16 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 2

Step 5:
2 goes into 7 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 21283
Subtract 6 from 7 to get 1.

The final result is 21283 with a remainder of 1.