what is the greatest prime factor of 2^34-2^28

[chini]

What is the greatest common factor of 2^34-2^28?

1) 2
2) 3
3) 5
4) 7
5) 11

I can't figure this out without doing out all of the math. Any pointers? Thanks

[Success]

(2^34-2^28)

if you pick out the common term
2^28 (2^6 - 1) = 2^28 ( 64-1)

2^28 (63 ) = take it term by term

2^28 has a prime number of 2.

63 / 3 = 21

21 / 3= 7

7 is a prime number, and thus, the highest.
I hope it is the answer............
And if it is not, could someone pls help us out.

[chini]

Thanks for the help. 7 is the answer; however why do you reason that it is 2^28 (2^6-1)? Where does the 1 come from? Thanks.

[rfernandez]

What is the greatest common factor of 2^34-2^28?

1) 2
2) 3
3) 5
4) 7
5) 11

Just to clarify, does the question actually read "What is the greatest prime factor...?" That's what I suspect. In order to find GCF, you need at least two numbers.

Thanks for the help. 7 is the answer; however why do you reason that it is 2^28 (2^6-1)? Where does the 1 come from? Thanks.

The 1 comes from factoring out the common factor of 2^28. As an analogy, consider factoring x^8 - x^3. Here, the common factor is x^3. Pulling that out gives x^3(x^5 - 1). Similarly, 2^34 - 2^28 yields 2^28(2^6 - 1).