Factoring exponents

[rbansal]

What is the greatest prime factor of 4^17 - 2^28?

a.2
b.3
c.5
d.7
e.11

Can someone please help me with this, with a step by step explanation

Thank you

[sourabh33]

D

4^17 - 2^28
2^34 - 2^28
2^28(2^6 -1)
2^28(64-1)
2^28(63)
2^28.3^2.7

Therefore 7 should be the greatest prime factor.

[rbansal]

D

4^17 - 2^28
2^34 - 2^28
2^28(2^6 -1)
2^28(64-1)
2^28(63)
2^28.3^2.7

Therefore 7 should be the greatest prime factor.

I Followed you all up until the last line can you clarify that please

[sourabh33]

The question is asking for the greatest prime factor

We can see from the prime factorization that the expression 4^17 - 2^28 can be factored in form of (2^28)x(3^2)x(7^1), therefore the greatest prime factor is 7.

Consider these examples

for integer 6 --> 6 = 2x3 therefore the greatest prime factor is 3
for integer 12 --> 12 = 2x2x3 therefore the greatest prime factor is 3 (and not 4 as 4 can be further factored as 2^2)