Here we can write 4^17 as 2^34
now taking 2^28 as factor the expression reduces to => 2^28 x 63
clearly 7 is the largest prime factor
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Thank you! I tried it in another way and I do not get why I got another answer than you did.

4^17 - 2^28 = 4^17 - 4^14 = 4^3 = 2^6

Because of that, I chose answer A.

We cannot simply subtract the terms.

4^17 - 4^14 = 4^14 (4^3 - 1) = 4^14*(64 - 1) = 4^14 * 63
Here we have taken 4^14 common from both the terms and written the remainder inside the brackets.

Added extra step:

\(4^{17}-2^{28}=2^{34}-2^{28}=2^{28}*2^6-2^{28}=2^{28}(2^6-1)=2^{28}*63=2^{28}*3^2*7\) --> greatest prime factor is 7.

So, we are factoring out \(2^{28}\) from \(2^{34}-2^{28}\).

Hope it's clear.
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2^34-2^28=2^28(2^6 -1)
=2^28(64-1)
=2^28(9*7)
Hence largest prime factor 7

A video explanation can be found here:
https://www.youtube.com/watch?v=gCL6DmaIqK4

The first step is noting that we want to work from a common base, i.e. instead of 4 and 2, we want 2^2 and 2. Now we have

(2^2)^17 - 2^28

What’s tested are your knowledge of exponent rules, factoring, and prime numbers. We have

2^34 – 2^28, which is

2^28(2^6 – 1) [note that 2^6 can be viewed more simply as 2^3*2^3, or 8*8], which is

2^28(64 – 1), which is

2^28 (63), which is

2^28 (3^2)(7)

Prime factors are 2, 3 and 7. Greatest prime factor is 7
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