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Exponents 2

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Joined: 06 May 2012
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13 May 2012, 20:47
Hi!! Pls I need some help with this question: What is the greatest prime factor of 4^17 - 2^28?

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

My answer is 7 but I am not sure.

Thank you
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Joined: 14 Apr 2009
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13 May 2012, 21:28
Hi shirley,

That's right.

4^17 should be rewritten as base 2: (2^2) ^ 17 = 2 ^ (17*2) = 2^34

2^34 - 2^28

Note: You cannot make that 2^ (34-28) = 2^6 = 64
You cannot do this.

To check this, always test it with smaller exponents like so:

2^5 - 2^2 = 2^3 ?
32 - 4 = 28 (not equal to 2^3 = 8)

So the way to reduce 2^34 - 2^28 is to factors out 2^28

2^28 ( 2^6 - 1) = 2^28 (64-1) = 2^28 (63)

Now just factor out that 63, which is 9*7. Since the 9 can be broken down into 3 and 3, you know the largest prime is the remaining 7.
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Re: Exponents 2   [#permalink] 13 May 2012, 21:28
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