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

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Math Expert
Joined: 02 Sep 2009
Posts: 46191
The greatest prime factor of 7^5+7^4+7^3 is: [#permalink]

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01 Mar 2017, 05:35
00:00

Difficulty:

35% (medium)

Question Stats:

58% (00:51) correct 42% (00:46) wrong based on 106 sessions

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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

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CEO
Joined: 12 Sep 2015
Posts: 2561
Re: The greatest prime factor of 7^5+7^4+7^3 is: [#permalink]

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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

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

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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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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.

_________________

Jeffery Miller

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

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: The greatest prime factor of 7^5+7^4+7^3 is: [#permalink]

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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.

_________________

Jeffery Miller

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:   [#permalink] 02 Mar 2017, 18:39
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