51663 ÷ 2 = 25831 R1
Alright, let's work through the division of 51663 by 2 step by step.

Step 1:
2 goes into 5 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 4 from 5 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: 25
Subtract 10 from 11 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 2

Step 3:
2 goes into 16 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 258
Subtract 16 from 16 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: 2583
Subtract 6 from 6 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 2

Step 5:
2 goes into 3 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 25831
Subtract 2 from 3 to get 1.

The final result is 25831 with a remainder of 1.