Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 100010000 and 1000100000 ?  Choose the correct answer:
A) 10
B) 11
C) 101
D) 1011
E) 10001
Starting from right count the positions of 1 s   100010000=(1*2^8) + (1*2^4)=(2^8 + 2^4)   similarly,   1000100000=(1*2^9)+(1*2^5)=(2^9 + 2^5)   Lets simplify them further,   (2^8 + 2^4)=2^4(2^4 +1)=2^4(16+1)=2^4(17)   (2^9 + 2^5)=2^5(2^4 +1)=2^5(16+1)=2^5(17)   The prime numbers common in both are 2 and 17, and the largest one is 17.   from the options, (10001) 10001=1*2^4+1*2^0=16+1= 
<gadget id="calculator">16+1</gadget>
<output>17</output>
17   Hence answer (10001).
<result>E</result>
Every digit of a number written in binary is either 0 or 1. To translate a number from binary, multiply the nth digit (reading from right to left) by 2^(n-1)
What is the largest prime number (written in binary) that is a factor of both 100010000 and 1000100000 ?