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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # For all integers p, <<p>> is the product of p's distinct prime factors

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

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Difficulty:   45% (medium)

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

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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>>

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Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

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<<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

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Manager  S
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]

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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.
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Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

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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 ??
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Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

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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  G
Joined: 31 Oct 2015
Posts: 95
Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

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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
VP  P
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]

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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

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Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

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

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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

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Re: For all integers p, <<p>> is the product of p's distinct prime factors  [#permalink]

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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

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

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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

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
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