59903 ÷ 2 = 29951 R1
Alright, let's work through the division of 59903 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 (9) of the dividend behind the 1 and repeat the process: 19 / 2

Step 2:
2 goes into 19 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 29
Subtract 18 from 19 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 2

Step 3:
2 goes into 19 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 299
Subtract 18 from 19 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 2

Step 4:
2 goes into 10 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 2995
Subtract 10 from 10 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: 29951
Subtract 2 from 3 to get 1.

The final result is 29951 with a remainder of 1.