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Prime factor

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Prime factor [#permalink] New post 20 Dec 2005, 07:59
How to solve this?

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

(a) 2
(b) 3
(c) 5
(d) 7
(e) 11
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 [#permalink] New post 20 Dec 2005, 08:14
4^14(4^3-1)

4^14 x 63= 4^14 x 7x3x3

Answer 7

D
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 [#permalink] New post 20 Dec 2005, 08:21
I am not that fast, can you eludcidate please?
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 [#permalink] New post 20 Dec 2005, 08:50
4^17 - 2^28 = 4^17 - 4^14 = 4^14 (4^3 - 1), thats the key

4^14 will have the smallest prime possibble 2, but

4^3 - 1 = 63 = 7*3*3, so the greatest prime is 7
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 [#permalink] New post 20 Dec 2005, 09:00
old_dream_1976 wrote:
4^14(4^3-1)

4^14 x 63= 4^14 x 7x3x3

Answer 7

D


Nice..... :-D
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 [#permalink] New post 20 Dec 2005, 10:02
Good job old dream... I agree w/ 7
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 [#permalink] New post 20 Dec 2005, 11:50
Yup, agree with old dream's working. 7 it is
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 [#permalink] New post 20 Dec 2005, 12:58
4^17 - 2^28 ===>2^34*2^28

==>2^28(2^6-1)

==>2^28*64-1

==>2^28*7*3^2

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 [#permalink] New post 20 Dec 2005, 18:55
2^28(2^6 - 1)
2^26*63
2^26*21*3
2^26*7*3*3
7 is the greatest prime factor.
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 [#permalink] New post 20 Dec 2005, 19:04
You will notice 4^17 = 2^34. So the question becomes 2^34 - 2^28 = 2^28(2^6-1) = 2^28(63)

The prime factors are 2^28 * 3 * 21 = 2^28 * 3 * 3 * 7

Greatest prime factor = 7
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Re: Prime factor [#permalink] New post 23 Dec 2005, 00:46
sandalphon wrote:
How to solve this?

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

(a) 2
(b) 3
(c) 5
(d) 7
(e) 11


= 2^34 - 2^28
= 2^28(2^6-1)
= 2^28 (64-1)
= 2^28 * 63
= 2 ^28 * 7 * 9
= 2^ 28 * 7 * 3^2
So 7 is the greatest prime factor.
Re: Prime factor   [#permalink] 23 Dec 2005, 00:46
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