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For all integers p, <<p>> is the product of p's distinct prime factors
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04 Nov 2019, 23:53
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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>>
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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 00:46
<<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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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 01:11
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. Eliminating answer choices: (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
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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 ??
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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 02:34
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>>



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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 02:43
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.



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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 05:28
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 Answer (D)



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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 06:53
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



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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 07:50
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.



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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 08:42
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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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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05 Nov 2019, 12:15
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
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Re: For all integers p, <<p>> is the product of p's distinct prime factors
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