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

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Manager
Joined: 09 Jun 2015
Posts: 91
Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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14 Mar 2016, 08:30
student26 wrote:
What is the greatest prime factor of 4^17 - 2^28?

A. 2
B. 3
C. 5
D. 7
E. 11

It can be written as 2^34 - 2^28 = 2^28*(2^6 - 1) = 2^28*63 = 2^28 * 3^2 * 7
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Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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16 Mar 2016, 02:36
Here we can write 4^17 as 2^34
now taking 2^28 as factor the expression reduces to => 2^28 x 63
clearly 7 is the largest prime factor
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Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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19 Apr 2016, 18:17
Flexxice wrote:
What is the greatest prime factor of 4^17 - 2^28?

A) 2

B) 3

C) 5

D) 7

E) 11

First of all 4^17 = (2^2)^17 = 2^34

So, 4^17 - 2^28 = 2^34 - 2^28
= 2^28(2^6 - 1) [factored out 2^28]
= 2^28(2^3 + 1)(2^3 - 1) [factored again]
= 2^28(8 + 1)(8 - 1) [evaluated]
= 2^28(9)(7) [evaluated]
= 2^28(3)(3)(7)

So, as you can see, the greatest prime factor is 7

Cheers,
Brent
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Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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19 Apr 2016, 21:21
GMATPrepNow wrote:
Flexxice wrote:
What is the greatest prime factor of 4^17 - 2^28?

A) 2

B) 3

C) 5

D) 7

E) 11

First of all 4^17 = (2^2)^17 = 2^34

So, 4^17 - 2^28 = 2^34 - 2^28
= 2^28(2^6 - 1) [factored out 2^28]
= 2^28(2^3 + 1)(2^3 - 1) [factored again]
= 2^28(8 + 1)(8 - 1) [evaluated]
= 2^28(9)(7) [evaluated]
= 2^28(3)(3)(7)

So, as you can see, the greatest prime factor is 7

Cheers,
Brent

Thank you! I tried it in another way and I do not get why I got another answer than you did.

4^17 - 2^28 = 4^17 - 4^14 = 4^3 = 2^6

Because of that, I chose answer A.
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What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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19 Apr 2016, 22:04
Flexxice wrote:
GMATPrepNow wrote:
Flexxice wrote:
What is the greatest prime factor of 4^17 - 2^28?

A) 2

B) 3

C) 5

D) 7

E) 11

First of all 4^17 = (2^2)^17 = 2^34

So, 4^17 - 2^28 = 2^34 - 2^28
= 2^28(2^6 - 1) [factored out 2^28]
= 2^28(2^3 + 1)(2^3 - 1) [factored again]
= 2^28(8 + 1)(8 - 1) [evaluated]
= 2^28(9)(7) [evaluated]
= 2^28(3)(3)(7)

So, as you can see, the greatest prime factor is 7

Cheers,
Brent

Thank you! I tried it in another way and I do not get why I got another answer than you did.

4^17 - 2^28 = 4^17 - 4^14 = 4^3 = 2^6

Because of that, I chose answer A.

Hi,
you are wrong in the highlighted portion--
$$\frac{4^{17}}{4^{14}}= 4^{17-14} =4^3$$
$$4^{17} - 4^{14} = 4^{14}(4^3-1) = 4^{14} *(64-1) = 4^{14}*63= 4^{14}*7*9..$$
You can not subtract the way you have done, it can be done ONLY if two terms are being divided as shown above..

a simpler examplewill be
$$2^3 -2^1$$.. as per you it will be$$2^2=4.$$.
BUT $$2^3-2^1=8-2=6..$$
hope it helps
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Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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21 Apr 2016, 01:57
Flexxice wrote:

Thank you! I tried it in another way and I do not get why I got another answer than you did.

4^17 - 2^28 = 4^17 - 4^14 = 4^3 = 2^6

Because of that, I chose answer A.

We cannot simply subtract the terms.

4^17 - 4^14 = 4^14 (4^3 - 1) = 4^14*(64 - 1) = 4^14 * 63
Here we have taken 4^14 common from both the terms and written the remainder inside the brackets.
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Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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15 Mar 2017, 17:40
Bunuel wrote:
student26 wrote:
What is the greatest prime factor of 4^17 - 2^28?

A. 2
B. 3
C. 5
D. 7
E. 11

$$4^{17}-2^{28}=2^{34}-2^{28}=2^{28}(2^6-1)=2^{28}*63=2^{28}*3^2*7$$ --> greatest prime factor is 7.

Why is it (2^6-1)?
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Posts: 56233
Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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16 Mar 2017, 07:07
1
Aline2289 wrote:
Bunuel wrote:
student26 wrote:
What is the greatest prime factor of 4^17 - 2^28?

A. 2
B. 3
C. 5
D. 7
E. 11

$$4^{17}-2^{28}=2^{34}-2^{28}=2^{28}(2^6-1)=2^{28}*63=2^{28}*3^2*7$$ --> greatest prime factor is 7.

Why is it (2^6-1)?

$$4^{17}-2^{28}=2^{34}-2^{28}=2^{28}*2^6-2^{28}=2^{28}(2^6-1)=2^{28}*63=2^{28}*3^2*7$$ --> greatest prime factor is 7.

So, we are factoring out $$2^{28}$$ from $$2^{34}-2^{28}$$.

Hope it's clear.
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Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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21 Mar 2017, 06:10
1
student26 wrote:
What is the greatest prime factor of 4^17 - 2^28?

A. 2
B. 3
C. 5
D. 7
E. 11

We need to determine the greatest prime factor of 4^17 – 2^28. We can start by breaking 4^17 into prime factors.

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

Now our equation is as follows:

2^34 – 2^28

Note that the common factor in each term is 2^28; thus, the expression can be simplified as follows:

2^28(2^6 – 1)

2^28(64 – 1)

2^28(63)

2^28 x 9 x 7

2^28 x 3^2 x 7

We see that the greatest prime factor must be 7.

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Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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27 Aug 2017, 08:52
2^34-2^28=2^28(2^6 -1)
=2^28(64-1)
=2^28(9*7)
Hence largest prime factor 7
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Re: What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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28 Sep 2018, 00:44
student26 wrote:
What is the greatest prime factor of 4^17 - 2^28?

A. 2
B. 3
C. 5
D. 7
E. 11

2^2^(17) = 2^34

2^28 (2^6 - 1 ) = 2^28 (64 - 1) = 2^28 * 63 = 2^28 * 3^2 * 7

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What is the greatest prime factor of 4^17 - 2^28?  [#permalink]

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24 Nov 2018, 15:18
A video explanation can be found here:

The first step is noting that we want to work from a common base, i.e. instead of 4 and 2, we want 2^2 and 2. Now we have

(2^2)^17 - 2^28

What’s tested are your knowledge of exponent rules, factoring, and prime numbers. We have

2^34 – 2^28, which is

2^28(2^6 – 1) [note that 2^6 can be viewed more simply as 2^3*2^3, or 8*8], which is

2^28(64 – 1), which is

2^28 (63), which is

2^28 (3^2)(7)

Prime factors are 2, 3 and 7. Greatest prime factor is 7
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What is the greatest prime factor of 4^17 - 2^28?   [#permalink] 24 Nov 2018, 15:18

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