amorphous wrote:

If \(x = 2^7^4 - 2^7^0\), what is the largest prime factor of x?

A)2

B)3

C)5

D)7

E)11

Given: x = 2^74 - 2^70

Factor 2^70 from right side to get: x = 2^70(2^4 - 1)

Evaluate to get: x = 2^70(16 - 1)

Simplify to get: x = (2^70)(15)

Factor 15 to get: x = (2^70)(3)(5)

So, there are 3 different prime factors: 2, 3 and 5

The greatest prime is 5

Answer: C

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

If you enjoy my solutions, you'll like my GRE prep course.

Sign up for GRE Question of the Day emails