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# the greatest prime factor of 4^17 - 2^28 ? 2 3 5 7 11

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VP
Joined: 29 Apr 2003
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the greatest prime factor of 4^17 - 2^28 ? 2 3 5 7 11 [#permalink]

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14 Apr 2006, 17:02
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the greatest prime factor of 4^17 - 2^28 ?

2
3
5
7
11

Kudos [?]: 30 [0], given: 0

Manager
Joined: 09 Feb 2006
Posts: 129

Kudos [?]: 8 [0], given: 0

Location: New York, NY

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14 Apr 2006, 18:04
What is the greatest prime factor of 4^17 - 2^28 ?

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

2^34 - 2^28 = 2^28 (2^6 - 1) = 2^28 (64 - 1) = 63*(2^28)

Prime factors are 2,3,and 7. Therefore, answer is 7.

Kudos [?]: 8 [0], given: 0

14 Apr 2006, 18:04
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