What is the greatest prime factor

[prengasn]

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

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

I apreciate an expanation.

[Kweku.Amoako]

4^17 - 2^28.....the trick here is to simplify and break the expression down into prime factors

4^17 = (2^2) ^17 = 2^34

so the problem becomes 2^34 - 2^28

at this point we can factorize out 2^28

there 2^34 - 2^28 = 2^28( (2^6) - 1)

we know 2^6 = 64 there 2^6 -1 = 63

so 2^34 - 2^28 = 2^28 ( 63 ) = 2^28 ( 7 * 9 ) = 2^28(7* 3^2)

so the prime factors are 2, 3 and 7 and there it's obvious the answer is 7

[prengasn]

Thanks a lot. Great explanation.

[RonPurewal]

please search for problems before you post them in the forum. this particular problem has been posted almost ten different times in the last couple of years.

here are two:

what-is-the-greatest-prime-factor-of-4-17-2-28-t411.html

what-is-the-greatest-prime-factor-of-4-17-2-28-t346.html

the latter of these two contains links to about 5 more versions, too.