It is currently 23 Feb 2018, 04:24

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# How many positive distinct prime factors does 5^20 + 5^17 have?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 26 Aug 2014
Posts: 3
How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

### Show Tags

04 Dec 2014, 00:32
6
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

65% (00:33) correct 35% (00:46) wrong based on 187 sessions

### HideShow timer Statistics

How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five
[Reveal] Spoiler: OA
Senior Manager
Joined: 13 Jun 2013
Posts: 278
Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

### Show Tags

04 Dec 2014, 00:43
2
This post was
BOOKMARKED
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five

$$5^{20} + 5^{17}$$ = $$5^{17}(5^3+1)$$

=$$5^{17}(125+1)$$
=$$5^{17} (126)$$
=$$5^{17} .2.7.3^2$$
thus total number of distinct prime factors are 4 (2,3,5,7)
Intern
Joined: 23 Jul 2013
Posts: 15
Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

### Show Tags

31 Jan 2016, 17:59
manpreetsingh86 wrote:
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five

$$5^{20} + 5^{17}$$ = $$5^{17}(5^3+1)$$

=$$5^{17}(125+1)$$
=$$5^{17} (126)$$
=$$5^{17} .2.7.3^2$$
thus total number of distinct prime factors are 4 (2,3,5,7)

Hi,

Shouldn't it be 1, 2, 3, 5 and 7? Please confirm. Thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 43892
Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

### Show Tags

31 Jan 2016, 21:17
Meetup wrote:
manpreetsingh86 wrote:
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five

$$5^{20} + 5^{17}$$ = $$5^{17}(5^3+1)$$

=$$5^{17}(125+1)$$
=$$5^{17} (126)$$
=$$5^{17} .2.7.3^2$$
thus total number of distinct prime factors are 4 (2,3,5,7)

Hi,

Shouldn't it be 1, 2, 3, 5 and 7? Please confirm. Thanks.

1 is NOT a prime number.

Check here for more: math-number-theory-88376.html

Hope it helps.
_________________
Retired Moderator
Joined: 12 Aug 2015
Posts: 2426
GRE 1: 323 Q169 V154
Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

### Show Tags

07 Jan 2017, 18:20
$$5^{17}+5^{20}=> 5^{17}(5^3+1) = 5^{17}*126=> 2*3^2*5^{17}*7$$
So it has 4 prime factors.
Hence D

_________________

Getting into HOLLYWOOD with an MBA

Stone Cold's Mock Tests for GMAT-Quant(700+)

BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 519
Location: India
Concentration: Marketing
GMAT 1: 710 Q49 V36
Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

### Show Tags

09 Feb 2018, 02:29
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five

5^20 + 5^ 17

take 5^17 common on both sides of the sign = 5^17( 5^3 + 1) = 5^17( 125+1) = 5^17 (126)

14 x 9 = 126 so prime are 2,3,7
5^17 prime is 5

prime factors are 5, 2, 3, 7

1 is not prime
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016
Re: How many positive distinct prime factors does 5^20 + 5^17 have? [#permalink]

### Show Tags

12 Feb 2018, 16:32
pbarrocas wrote:
How many positive distinct prime factors does 5^20 + 5^17 have?

A) One
B) Two
C) Three
D) Four
E) Five

We can simplify the given expression by first factoring 5^17 as a common factor:

5^17(5^3 + 1)

5^17(126)

5^17 x 2 x 63

5^17 x 2 x 3^2 x 7

Thus, 5^20 + 5^17 has 4 distinct prime factors.

_________________

Jeffery Miller

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

Re: How many positive distinct prime factors does 5^20 + 5^17 have?   [#permalink] 12 Feb 2018, 16:32
Display posts from previous: Sort by