10971 ÷ 2 = 5485 R1
Alright, let's work through the division of 10971 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 (0) of the dividend behind the 1 and repeat the process: 10 / 2

Step 2:
2 goes into 10 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 10 from 10 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 2

Step 3:
2 goes into 9 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 54
Subtract 8 from 9 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: 548
Subtract 16 from 17 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 2

Step 5:
2 goes into 11 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 5485
Subtract 10 from 11 to get 1.

The final result is 5485 with a remainder of 1.