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What is the greatest prime factor of 49^19 - 7^35

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What is the greatest prime factor of 49^19 - 7^35  [#permalink]

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New post 03 Jan 2017, 11:40
3
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A
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C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:35) correct 39% (01:32) wrong based on 111 sessions

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Re: What is the greatest prime factor of 49^19 - 7^35  [#permalink]

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New post 03 Jan 2017, 13:07
3
stonecold wrote:
What is the greatest prime factor of \(49^{19}-7^{35}\)
A)2
B)3
C)7
D)13
E)19


\((7^2)^{19} - 7^{35} = 7^{38} - 7^{35} = 7^{35}(7^3 - 1) = 7^{35}*342 = 7^{35}*2*3^2*19\)

Answer E
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What is the greatest prime factor of 49^19−7^35  [#permalink]

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New post 27 Jan 2019, 22:17
What is the greatest prime factor of 49^19−7^35

A) 2
B) 3
C) 7
D) 13
E) 19
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Re: What is the greatest prime factor of 49^19−7^35  [#permalink]

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New post 27 Jan 2019, 22:32
1
Gmatprep550 wrote:
What is the greatest prime factor of 49^19−7^35

A)2
B)3
C)7
D)13
E)19

I am not able to understand solution for this, can any one help


Would like to share my thoughts on this

\(49^{19}−7^{35}\)

Always reduce the terms in their lowest factors, said that

\(7^{2* 19} - 7^{35}\)

\(7^{35} ( 7^3 - 1)\)

\(7^{35}\), will always have 7 has a factor

\(7^3 - 1\), can be reduced to 342, which can be written as \(2 * 3^2 * 19\)

So out of this bunch 2,3,7 and 19

E is the largest prime number
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Re: What is the greatest prime factor of 49^19 - 7^35  [#permalink]

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New post 27 Jan 2019, 23:36
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Re: What is the greatest prime factor of 49^19 - 7^35  [#permalink]

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New post 28 Jan 2019, 02:15
stonecold wrote:
What is the greatest prime factor of \(49^{19}-7^{35}\)

A) 2
B) 3
C) 7
D) 13
E) 19



\(49^{19}-7^{35}\)

7^35( 7^3-1)
7^35* 342
342= 2*3^2*19^1

so greatest prime factor
7^35 * 2*3^2*19^1

IMO E 19
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Re: What is the greatest prime factor of 49^19 - 7^35  [#permalink]

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New post 22 Nov 2019, 17:11
Top Contributor
stonecold wrote:
What is the greatest prime factor of \(49^{19}-7^{35}\)

A) 2
B) 3
C) 7
D) 13
E) 19


49^19 - 7^35 = (7^2)^19 - 7^35
= 7^38 - 7^35
= (7^35)(7^3 - 1)
= (7^35)(343 - 1)
= (7^35)(342)
= (7^35)(2)(3)(3)(19)

Answer: E

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Brent
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Re: What is the greatest prime factor of 49^19 - 7^35   [#permalink] 22 Nov 2019, 17:11
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