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Exponents / prime factors question

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Exponents / prime factors question [#permalink] New post 07 Oct 2007, 16:43
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This one is from the GMAC practice test. Still can't figure it out - might be mind numbness setting in...

What is the greatest prime factor of:

4^17 - 2^28

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

Please explain how you arrived at your answer. Thanks a bunch!
-Jackie
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 [#permalink] New post 07 Oct 2007, 17:00
HEHE. I just took the GMATPrep 2 and got this problem wrong. Why did I get it wrong? Simple, careless mistake with the exponent rule: x^y * x^z = x ^(y+z)

But this question has a subtraction so that rule does not apply. If you did what I did, you would choose 2 as the answer. As soon as I saw my careless mistake, I knew how to get the correct answer

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

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

2^28 has 2 as the highest prime factor
63 = 7*9 = 7*3*3 so 7 is the highest prime factor. Answer is 7 D.
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Re: Exponents / prime factors question [#permalink] New post 07 Oct 2007, 18:14
jthong wrote:
This one is from the GMAC practice test. Still can't figure it out - might be mind numbness setting in...

What is the greatest prime factor of:

4^17 - 2^28

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

Please explain how you arrived at your answer. Thanks a bunch!
-Jackie


also D,

same reasoning as of mayonnai5e.
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Exponents / prime factors question [#permalink] New post 07 Oct 2007, 18:19
Thanks! I'm still not getting the bit about 64-1... Can you explain a bit more?
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Re: Exponents / prime factors question [#permalink] New post 07 Oct 2007, 21:57
jthong wrote:
Thanks! I'm still not getting the bit about 64-1... Can you explain a bit more?


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

Make prime factorization for 63:

3 x 3 x 7 = 63,


so 2^34 - 2^28= 2^28 x 3 x 3 x 7

among prime factors: 2, 3, 7. Seven is the biggest.

:)
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 [#permalink] New post 08 Oct 2007, 06:38
not sure how you got 2^6-1 from 2^28?
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Re: Exponents / prime factors question [#permalink] New post 08 Oct 2007, 10:50
jthong wrote:
This one is from the GMAC practice test. Still can't figure it out - might be mind numbness setting in...

What is the greatest prime factor of:

4^17 - 2^28

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

Please explain how you arrived at your answer. Thanks a bunch!
-Jackie


4^17 can be rewritten as (2^2)^17 ---> 2^34

So we now have 2^34-2^28. Factor---> 2^28(2^6-1) U should at least know that 2^5=32, itd just be helpful for the GMAT.

So 2^6 is equals 64. 64-1=63. Greatest prime factor of 63 is 7. (7*9)

So ans is D.
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 [#permalink] New post 08 Oct 2007, 10:53
jingy77 wrote:
not sure how you got 2^6-1 from 2^28?


2^28(2^6-1) ---> is the same as 2^28*2^6 -2^28---> 2^34-2^28

When multiplying numbers w/ same base we add exponents.

Ex/ x^2*x^3=x^5 ---> 2+3=5.


Same with this here. 28+6=34.
  [#permalink] 08 Oct 2007, 10:53
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