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The greatest prime factor of 7^5+7^4+7^3 is:

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The greatest prime factor of 7^5+7^4+7^3 is:  [#permalink]

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New post 01 Mar 2017, 05:35
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (00:52) correct 39% (00:46) wrong based on 113 sessions

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Re: The greatest prime factor of 7^5+7^4+7^3 is:  [#permalink]

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New post 01 Mar 2017, 06:05
1
Top Contributor
Bunuel wrote:
The greatest prime factor of 7^5 + 7^4 + 7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30


\(7^5 + 7^4 + 7^3 = 7^3(7^2 + 7^1 + 1)\)
\(= 7^3(49 + 7 + 1)\)
\(= 7^3(57)\)
\(=7^3(3)(19)\)
\(= (7)(7)(7)(3)(19)\)

The greatest prime factor is 19

Answer: C
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Re: The greatest prime factor of 7^5+7^4+7^3 is:  [#permalink]

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New post 01 Mar 2017, 11:40
Bunuel wrote:
The greatest prime factor of 7^5+7^4+7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30


7^5+7^4+7^3

= 7^3 ( 7^2 + 7 +1 )

= 7^3*57

= 7^3*( 3 * 19 )

Thus, the greatest prime number is 19..

Hence, answer must be (C) Between 10 and 20
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Re: The greatest prime factor of 7^5+7^4+7^3 is:  [#permalink]

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New post 02 Mar 2017, 18:36
Bunuel wrote:
The greatest prime factor of 7^5+7^4+7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30


Let’s simplify the given expression:

7^5+7^4+7^3

7^3(7^2 + 7^1 + 1)

7^3(49 + 7 + 1)

7^3(57) = 7^3 x 19 x 3

Thus, the greatest prime factor of 7^5+7^4+7^3 is 19, which is between 10 and 20.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
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Target Test Prep Representative
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Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: The greatest prime factor of 7^5+7^4+7^3 is:  [#permalink]

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New post 02 Mar 2017, 18:39
1
Bunuel wrote:
The greatest prime factor of 7^5+7^4+7^3 is:

A. Less than 4
B. Between 4 and 10
C. Between 10 and 20
D. Between 20 and 30
E. Greater than 30


Let’s simplify the given expression:

7^5+7^4+7^3

7^3(7^2 + 7^1 + 1)

7^3(49 + 7 + 1)

7^3(57) = 7^3 x 19 x 3

Thus, the greatest prime factor of 7^5+7^4+7^3 is 19, which is between 10 and 20.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: The greatest prime factor of 7^5+7^4+7^3 is: &nbs [#permalink] 02 Mar 2017, 18:39
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