To answer this we must find the prime factorization of 4^17 - 2^28Kuros wrote:What is the greatest prime factor of 4^17 - 2^28?
a)2
b)3
c)5
d)7
e)11
To do this, we'll apply to algebraic factoring techniques (and some exponent rules).
Since 4 is not prime, let's first take 4^17 and replace 4 with 2^2
When we do this, we get (2^2)^17 - 2^28
We can now apply the Power of a Power Rule to rewrite this as 2^34 - 2^28
From here, let's factor out 2^28 to get 2^28(2^6 - 1)
2^6 evaluates to be 64, so we get: 2^28(64 - 1)
This equals 2^28(63)
We can find the prime factorization of 63 to write this as (2^28)(3)(3)(7)
So, 4^17 - 2^28 = (2^28)(3)(3)(7), which means the greatest prime factor is 7
Answer: D
