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

Question

Competition Mode Question For all integers 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>>

madgmat2019 · Answer

<<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

vg18 · Answer

For all integers 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. Eliminating answer choices: (A) <<2>>=2 (B) <<3>>=3 (C) <<8>>=2 (D) <<12>>=2*3=6. Correct (E) <<14>> =2*7=14.

unraveled · Answer

For all integers 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 ??

Archit3110 · Answer

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, <

> 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>>

suchithra · Answer

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 <

>. We need an answer that has distinct prime factors as 2&3 only. Of the answer choices, <<12>> = 6 Therefore, answer is D.

exc4libur · Answer

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 Answer (D)

Raxit85 · Answer

For all integers 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

eakabuah · Answer

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.

CareerGeek · Answer

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

lacktutor · Answer

For all integers 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

jppresa · Answer

The question stem contains odd symbols, so it’s testing functions. Follow the directions carefully. The function <

> is the product of p's distinct prime factors. The distinct prime factors of 24 are 2 and 3, so <<24>> = 2 × 3 = 6. The distinct prime factors of 54 are 2 and 3, so <<54>> = 2 × 3 = 6. Therefore, the greatest common factor of <<24>> and <<54>> is 6. Check each of the answer choices, looking for the one that equals 6. Choice A is <<2>> = 2, so eliminate choice A. Choice B is <<3>> = 3, so eliminate choice B. Choice C is <<8>> = 2, so eliminate choice C. Choice D is <<12>> = 2 × 3 = 6, so keep choice D. Choice E is <<14>> = 2 × 7 = 14, so eliminate choice E. The correct answer is choice D.

CrackverbalGMAT · Answer

Solution:

Distinct prime factors of 24 are 2,3

<<24>> = 2*3 = 6

Distinct prime factors of 54 are 2,3

<<54>> = 2*3 = 6

Greatest common factors of 6 ,6 is 6

Option A and B can be eliminated as they are prime values. Option c has value of 2 and not 6 and can be eliminated.

Option d = <<12>>

= 2*3 = 6
Hence option (d)

Devmitra Sen
GMAT SME

CEdward · Answer

So to be clear, had the answers not included << >> then B would be correct?

Kinshook · Answer

Given: For all integers p, <

> is the product of p's distinct prime factors. Asked: What is the greatest common factor of <<24>> and <<54>>? 24=2^3*3 <<24>>=2*3=6 54=3^3*2 <<54>>=2*3=6 GCF(<<24>>,<<54>>)=6 <<12>>=2*3=6 IMO D Posted from my mobile device

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

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

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