1266 ÷ 2 = 633 R0
Alright, let's work through the division of 1266 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 (2) of the dividend behind the 1 and repeat the process: 12 / 2

Step 2:
2 goes into 12 6 times with a remainder of 0.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 12 from 12 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 2

Step 3:
2 goes into 6 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 63
Subtract 6 from 6 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 2

Step 4:
2 goes into 6 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 633
Subtract 6 from 6 to get 0.

The final result is 633 with a remainder of 0.