lukeposada wrote:Need some help please!
What is the greatest prime factors of 4^17 - 2^28?
Answer is 7
To answer this we must find the prime factorization of 4^17 - 2^28
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 evalates 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
