GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 01 Apr 2020, 23:37

### 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

# For all integers p, <<p>> is the product of p's distinct prime factors

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62469
For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

04 Nov 2019, 23:53
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:33) correct 40% (01:51) wrong based on 80 sessions

### HideShow timer Statistics

Competition Mode Question

For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?

(A) <<2>>
(B) <<3>>
(C) <<8>>
(D) <<12>>
(E) <<14>>

_________________
Senior Manager
Joined: 01 Mar 2019
Posts: 484
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GMAT 1: 580 Q48 V21
GPA: 4
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 00:46
1
1
<<24>> = 2^3 * 3=6

<<54>> = 3^3 * 2=6

Hcf of 6and6 is 6

The only option with a multiple of 6 is 12

OA :D

Posted from my mobile device
Manager
Joined: 30 Nov 2017
Posts: 67
GMAT 1: 690 Q49 V35
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 01:11
1
For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?
<<24>>= 6( as 2&3 are distinct prime factors)
<<54>>= 6( as 2&3 are distinct prime factors)
GCD(6,6) is 6.
(A) <<2>>=2
(B) <<3>>=3
(C) <<8>>=2
(D) <<12>>=2*3=6. Correct
(E) <<14>> =2*7=14.
Director
Joined: 07 Mar 2019
Posts: 907
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 02:09
For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?

(A) <<2>>
(B) <<3>>
(C) <<8>>
(D) <<12>>
(E) <<14>>

$$<<24>> = 2^3 * 3$$
$$<<54>> = 2 * 3^3$$

What i understood is that <<24>> must be a multiple of distinct prime numbers, so each prime must occur only one and not a multiple of multiple times of a prime number.

For example let a number is 28
So 28 = 2^2 * 7
thus <<28>> = 7 * 2 = 14.

Is my understanding is correct ??
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6048
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 02:34
1
greatest common factor of <<24>> and <<54>>
6, 6
answer option shall have prime factors of 2,3
IMO D; 12

For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?

(A) <<2>>
(B) <<3>>
(C) <<8>>
(D) <<12>>
(E) <<14>>
Manager
Joined: 31 Oct 2015
Posts: 95
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 02:43
1
Distinct prime factors of <<24>> is 2 & 3. There <<24>>=6
Similarly, distinct prime factors of <<54>> is 2& 3. Therefore <<54>>= 6.

We notice that all answer choices are in the form of <<p>>. We need an answer that has distinct prime factors as 2&3 only.

Of the answer choices, <<12>> = 6
Therefore, answer is D.
VP
Joined: 24 Nov 2016
Posts: 1350
Location: United States
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 05:28
1
Quote:
For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?

(A) <<2>>
(B) <<3>>
(C) <<8>>
(D) <<12>>
(E) <<14>>

pfactors(24)=(12*2…2^2*3*2…2^3*3); distinctpfactors(24)=(2,3); <<24>>=(2*3)=6
pfactors(54)=(6*9…2*3*3^2…2*3^3); distinctpfactors(54)=(2,3); <<54>>=(2*3)=6
gcf(6,6)=6; <<12>>: pfactors(12)=(2^2*3); dpfactors(12)=(2*3); <<12>>=(2*3)=6

Director
Joined: 22 Feb 2018
Posts: 595
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 06:53
1
For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?

Distinct prime factors of <<24>> = 6 (2,3)
Distinct prime factors of <<54>> = 6 (2,3)
GCF of <<24>> and <<54>> = 6

(A) <<2>> = 2,
(B) <<3>> = 3
(C) <<8>> = 2
(D) <<12>> = 6
(E) <<14>> = 7

Imo. D
CR Forum Moderator
Joined: 18 May 2019
Posts: 797
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 07:50
1
24=2^3 * 3
hence <<24>> = 2*3=6

54=2 * 3^3
hence <<54>>=2*3=6

The GCF of <<24>> and <<54>> = 6
This is equivalent to <<12>>=2*3=6

The answer is therefore D.
VP
Joined: 20 Jul 2017
Posts: 1482
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 08:42
1
24= 2^3*3
—> <<24>> = 2*3 = 6

54 = 3^3*2
—> <<54>> = 3*2 = 6

Greatest common factor of <<24>> and <<54>> is GCF(6, 6) = 6

(A) <<2>> = 2
(B) <<3>> = 3
(C) 8 = 2^3. So, <<8>> = 2
(D) 12 = 2^2*3. So, <<12>> = 2*3 = 6
(E) 14 = 2*7. So, <<14>> = 2*7 = 14

IMO Option D

Posted from my mobile device
Director
Joined: 25 Jul 2018
Posts: 637
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

### Show Tags

05 Nov 2019, 12:15
1
For all integers p, <<p>> is the product of p's distinct prime factors. What is the greatest common factor of <<24>> and <<54>>?

$$24= 2^{3}*3$$
—> <<24>> = 2*3= 6

$$54= 2*3^{3}$$
—> <<54>>= 2*3= 6

GCF(6,6)= 6

A) <<2>> = 2
B) <<3>> = 3
C) <<8>> = 2
D) <<12>>= 2*3= 6
Correct
E) <<14>>= 2*7= 14

The answer is D

Posted from my mobile device
Re: For all integers p, <<p>> is the product of p's distinct prime factors   [#permalink] 05 Nov 2019, 12:15
Display posts from previous: Sort by

# For all integers p, <<p>> is the product of p's distinct prime factors

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne